1. Notes For The Course In Differential Geometry for the course in. differential geometry. These notes are from the course given in WIS in 19921993 academic year. http://www.wisdom.weizmann.ac.il/~yakov/Geometry

Lecture notes for the course in Differential Geometry These notes are from the course given in WIS in 1992-1993 academic year. Mostly they constitute a collection of definitions, formulations of most important theorems and related problems for self-control. Since that time, in 1996, I changed the order of exposition. Therefore the logical structure is not the same. Anyhow, I hope that these notes can still be useful for self-control. The general rule is always the same: if you do understand the problem, try to solve it. If you don't - disregard it The problems for exam are here First semester 1. Introduction to manifolds. Topolgical spaces, exotic topologies. Constructions (Cartesian product, quotient space, metric compatible with topology etc). Differentiable mappings of the Euclidean n-space. Diffeomorphisms. Definition of a smooth manifold. 1a. Supplement to Lecture 1. Matrix manifolds. Partitions of unity. Whitney (weak) embedding theorem. 2. Tangent vectors. Tangent bundle. Definition via classes of first-order-equivalent curves. Tangent maps (differentials of diffeomorphisms). Vector fields. Action of diffeomorphisms on vector fields. 3. Algebra of vector fields. Lie derivatives.

2. 53: Differential Geometry 53 differential geometry differential geometry is the language of modern physics as well as an area of mathematical delight. http://www.math.niu.edu/~rusin/known-math/index/53-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 53: Differential geometry Introduction Differential geometry is the language of modern physics as well as an area of mathematical delight. Typically, one considers sets which are manifolds (that is, locally resemble Euclidean space) and which come equipped with a measure of distances. In particular, this includes classical studies of the curvature of curves and surfaces. Local questions both apply and help study differential equations; global questions often invoke algebraic topology. History See e.g. Berger, M. "Riemannian geometry during the second half of the twentieth century", Jahresber. Deutsch. Math.-Verein. 100 (1998), no. 2, 45208. CMP1637246 Applications and related fields For differential topology, See 57RXX. For foundational questions of differentiable manifolds, See 58AXX Geometry of spheres is in the sphere FAQ . There is a separate section for detailed information about 52A55: Spherical Geometry A metric in the sense of differential geometry is only loosely related to the idea of a metric on a metric space Subfields Classical differential geometry Local differential geometry Global differential geometry, see also 51H25, 58-XX; for related bundle theory, See 55RXX, 57RXX

3. Notes On Differential Geometry By B. Csikós FAQ How to read these files? Answer The files below are postscript files compressed with gzip. differential geometry. Budapest Semesters in Mathematics http://www.cs.elte.hu/geometry/csikos/dif/dif.html

Differential Geometry Budapest Semesters in Mathematics Lecture Notes by Balázs Csikós FAQ: How to read these files? Answer: The files below are postscript files compressed with gzip . First decompress them by gunzip , then you can print them on any postscript printer, or you can use ghostview to view them and print selected (or all) pages on any printer. CONTENTS Unit 1. Basic Structures on R n , Length of Curves. Addition of vectors and multiplication by scalars, vector spaces over R, linear combinations, linear independence, basis, dimension, linear and affine linear subspaces, tangent space at a point, tangent bundle; dot product, length of vectors, the standard metric on R n ; balls, open subsets, the standard topology on R n , continuous maps and homeomorphisms; simple arcs and parameterized continuous curves, reparameterization, length of curves, integral formula for differentiable curves, parameterization by arc length. Unit 2. Curvatures of a Curve Convergence of k-planes, the osculating k-plane, curves of general type in R n , the osculating flag, vector fields, moving frames and Frenet frames along a curve, orientation of a vector space, the standard orientation of R n , the distinguished Frenet frame, Gram-Schmidt orthogonalization process, Frenet formulas, curvatures, invariance theorems, curves with prescribed curvatures.

4. Alfred Gray's Home Page This differential geometry web site is maintained in memory of http://math.cl.uh.edu/~gray

This Differential Geometry web site is maintained in memory of Professor Alfred Gray Costa's minimal surface The Mathematica miniprograms and Compressed sample notebooks for Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition , CRC Press (1998), (See CRC Catalog) Curvas y Superficies , Addison-Wesley Ibero-Americana (1994), Differentialgeometrie , Spektrum-Verlag (1994), Japanese Edition (1996), Italian Edition, 1998. are available SurfaceExplorer , a Mathematica application for viewing surfaces from differential geometry, is now available. Visit the space curve gallery, plane curve gallery, constant curvature surface gallery minimal surface gallery and the general surface gallery. For comments on this page, contact Michael Mezzino by email mezzino@math.cl.uh.edu. or his home page http://math.cl.uh.edu/~mezzino Files are also available via anonymous ftp at ftp://math.cl.uh.edu/

5. Differential Geometry. Honours 1996 Next Contents Contents. differential geometry. Honours 1996 http://www.maths.adelaide.edu.au/pure/mmurray/dg_hons/dg_hons.html

Next: Contents Contents Differential Geometry. Honours 1996 Michael Murray Contents Co-ordinate independent calculus. Introduction Smooth functions ... About this document ... Michael Murray

6. Michor, Peter, Publications Several books by Peter W. Michor et al. including "Foundations of differential geometry", Category Science Math Publications Online Texts...... F Kolár, Ivan; Slovák, Jan; Michor, Peter W. Natural operations in differentialgeometry. H Michor, Peter W. Topics in differential geometry. http://www.mat.univie.ac.at/~michor/listpubl.html

Publications of Peter W. Michor Reviews on articles of Peter Michor in Zentralblatt-MATH Reviews on articles of Peter Michor in MathSciNet (Mathematical Reviews). Call and technical advise to scan and put pre-TeX publications on the web. Monographs and Lecture Notes [A] Michor, Peter W.: Functors and categories of Banach spaces. Springer Lecture Notes 651, (1978), vi+99 pp., MR 80h:46116, Z 369.46069. Out of print. [B] Cigler, Johann; Losert, Viktor; Michor, Peter W.: Banach modules and functors on categories of Banach spaces. Lecture Notes in Pure and Applied Mathematics 46, Marcel Dekker Inc., New York, Basel, (1979), MR 80j:46112, Z 411.46044. Review in Bull. AMS 3,2 (1980) xv+282 pp., Orders to: Marcel Dekker, inc., 270, Madison Avenue, New York, N.Y.10016, tel (212)696-9000 [C] Michor, Peter W.: Manifolds of differentiable mappings. Shiva Mathematics Series 3, Shiva Publ., Orpington, (1980), iv+158 pp., MR 83g:58009, ZM 433.58001 Out of print. [D] Michor, Peter W.: Elementary catastrophe theory.

7. Workshop On Differential Geometry University of Adelaide, Australia; 2527 March 2002.Category Science Math Geometry Events Past Events......Workshop on differential geometry. Dates Monday 25th March Wednesday27th March 2002. Location Coffee Breaks will be held in http://www.maths.adelaide.edu.au/iga/wdg.html

Workshop on Differential Geometry Dates : Monday 25th March - Wednesday 27th March 2002. Location : Coffee Breaks will be held in Engineering and Mathematics Building, Room EM117. Lectures will be held in various locations. Coffee and Tea will be available from about 9am every day in EM117. Here is a map of campus. Organiser : Michael Eastwood (meastwoo@maths.adelaide.edu.au). There is no registration fee. All interested are welcome. Speakers Alan Carey (Australian National University) Michael Cowling (University of New South Wales) Tony Dooley (University of New South Wales) Michael Eastwood (Adelaide University) Klaus Ecker (Monash University) Min-Chun Hong (Australian National University) Gen Komatsu (Osaka University) Michael Murray (Adelaide University) Hyam Rubinstein (University of Melbourne) Paul Tod (University of Oxford) Neil Trudinger (Australian National University) Joseph Wolf (University of California at Berkeley) Programme The workshop will start on Monday at 10:15am and finish on Wednesday at 4:30pm. The programme is available here Titles and Abstracts They can be found here Funding There will be some financial support available to interstate participants, with graduate students being given priority.

8. Journal Of Differential Geometry Home Page International Press. presents Journal of differential geometry online.About the Journal of differential geometry. How do I subscribe? http://www.intlpress.com/JDG/

©Lehigh University ISSN 0022-040X Presented by International Press International Press presents Journal of Differential Geometry on-line About the Journal of Differential Geometry How do I subscribe? Who is involved in the JDG? ... License

9. Mathematics Archives - Topics In Mathematics - Differential Geometry saddle, the handkerchief surface, surfaces of revolution and canal surfaces. differential geometry and its Applications http://archives.math.utk.edu/topics/differentialGeom.html

Topics in Mathematics Differential Geometry AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases The Atlas of Harmonic Morphisms ADD. KEYWORDS: Bibliography, Open Problems, Classifications Boy's Surface Center for Geometry, Analysis, Numerics, and Graphics (GANG) ADD. KEYWORDS: Surfaces, knots, research papers, software Center for Gravitational Physics and Geometry ADD. KEYWORDS: Meetings, People, Journals, Preprints Cusps of Gauss Mappings ADD. KEYWORDS: the shoe surface, Menn's surface, the perturbed monkey saddle, the handkerchief surface, surfaces of revolution and canal surfaces Differential Geometry and its Applications ADD. KEYWORDS: Journal Differential Geometry and Quantum Physics , SFB 288, TU Berlin DOCUMENTA MATHEMATICA - Extra Volume ICM 1998 - Section: 5. Differential Geometry and Global Analysis ADD. KEYWORDS: Articles SOURCE: DOCUMENTA MATHEMATICA, Proceedings of the International Congress of Mathematicians TECHNOLOGY: Postscript and DVI readers Elementary Differential Geometry: Curves and Surfaces ADD. KEYWORDS:

10. Journal Of Differential Geometry The Journal of differential geometry is published quarterly. It contains researcharticles of the highest quality in all areas of pure and applied mathematics. http://www.intlpress.com/JDGonline/

Current Issue: Volume 50, Issue 3 The Journal of Differential Geometry is published quarterly. It contains research articles of the highest quality in all areas of pure and applied mathematics. Editorial board Submission Information On line subscription Register for e-mail Notification Browse Journals

11. ScienceDirect - Differential Geometry And Its Applications - List Of Issues differential geometry and its Applications ADD. http://www.sciencedirect.com/science/journal/09262245

This Feature requires JavaScript Register or Login: Password: Athens Login Differential Geometry and its Applications Bookmark this page as: http://www.sciencedirect.com/science/journal/09262245 = subscribed = non-subscribed = complimentary Volumes 11 - 18 Volume 18, Issue 2 , Pages 119-238 (March 2003) Volume 18, Issue 1 , Pages 1-117 (January 2003) Volume 17, Issues 2-3 , Pages 111-273 (September 2002) Volume 17, Issue 1 , Pages 1-110 (July 2002) Volume 16, Issue 3 , Pages 199-293 (May 2002) Volume 16, Issue 2 , Pages 95-198 (March 2002) Volume 16, Issue 1 , Pages 1-94 (January 2002) Volume 15, Issue 3 , Pages 203-287 (November 2001) Volume 15, Issue 2 , Pages 107-201 (September 2001) Volume 15, Issue 1 , Pages 1-106 (July 2001) Volume 14, Issue 3 , Pages 217-313 (May 2001) Volume 14, Issue 2 , Pages 113-216 (March 2001) Volume 14, Issue 1 , Pages 1-111 (January 2001) Volume 13, Issue 3 , Pages 213-319 (November 2000) Volume 13, Issue 2 , Pages 119-211 (September 2000) Volume 13, Issue 1 , Pages 1-118 (July 2000) Volume 12, Issue 3 , Pages 219-313 (May 2000) Volume 12, Issue 2

12. Journal Of Differential Geometry Journal of differential geometry. The Journal of differential geometry is publishedat Lehigh University. Call 610758-3750 to speak to editor CC Hsiung. http://www.lehigh.edu/~math/jdg.html

Journal of Differential Geometry The Journal of Differential Geometry is published at Lehigh University. Call 610-758-3750 to speak to editor C.C. Hsiung. Photos of the May 1996 conference at Harvard University celebrating the 30th anniversary of the journal and the 80th birthday of its founder, C.C. Hsiung, emeritus professor in the Lehigh University Department of Mathematics. JDG sponsors the annual Lehigh University Geometry/Topology Conference. JDG information People involved in JDG Submissions ... Journal of Differential Geometry Online

13. Differential Geometry - Dynamical Systems differential geometry Dynamical Systems. ISSN 1454-511X. DifferentialGeometry is a fully refereed research domain included in all http://vectron.mathem.pub.ro/dgds/

Differential Geometry - Dynamical Systems ISSN 1454-511X Differential Geometry is a fully refereed research domain included in all aspects of mathematics and its applications. The Electronic Journal "Differential Geometry - Dynamical Systems" is published in free electronic format by Balkan Society of Geometers, Geometry Balkan Press. Main Journal Papers Volume 1 (1999) Volume 2 (2000) Volume 3, no. 1 (2001) Volume 3, no. 2 (2001) ... Editors Mathematics Journals Applied Sciences (APPS) The Electronic Library of Mathematics (EMIS) Paper and Electronic Journals Comments welcome Last update: January 2003.

14. Differential Gometry And General Relativity Introduction to differential geometry and general relativity by Stefan Waner at Hofstra University in HTML.Category Science Math Publications Online Texts......Online introduction to differential geometry and general relativity. Introductionto differential geometry and General Relativity. http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html

Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields ... Download the latest version of the differential geometry/relativity notes in PDF format References and Suggested Further Reading (Listed in the rough order reflecting the degree to which they were used) Bernard F. Schutz, A First Course in General Relativity (Cambridge University Press, 1986) David Lovelock and Hanno Rund, Tensors, Differential Forms, and Variational Principles (Dover, 1989) Charles E. Weatherburn, An Introduction to Riemannian Geometry and the Tensor Calculus (Cambridge University Press, 1963) Charles W. Misner, Kip S. Thorne and John A. Wheeler, Gravitation (W.H. Freeman, 1973) Keith R. Symon

15. Natural Operations In Differential Geometry A systematic treatment of naturality in differential geometry requires to describe all natural bundles, and this is also http://rattler.cameron.edu/EMIS/monographs/KSM

The Electronic Library of Mathematics Mathematical Monographs For fastest access: Choose your nearest mirror site! Natural operations in differential geometry by Ivan Kolar, Jan Slovak and Peter W. Michor Paper version originally published by Springer-Verlag, Berlin, Heidelberg, New York, 1993 ISBN 3-540-56235-4 (Germany) Download the whole book as one file: HYPER-DVI ] (838,207 bytes) Postscript ] (1,330,587 bytes) PDF ] (2,945,143 bytes) The aim of this book is threefold: First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. Even though Ehresmann in his original papers from 1951 underlined the conceptual meaning of the notion of an $r$-jet for differential geometry, jets have been mostly used as a purely technical tool in certain problems in the theory of systems of partial differential equations, in singularity theory, in variational calculus and in higher order mechanics. But the theory of natural bundles and natural operators clarifies once again that jets are one of the fundamental concepts in differential geometry, so that a thorough treatment of their basic properties plays an important role in this book. We also demonstrate that the central concepts from the theory of connections can very conveniently be formulated in terms of jets, and that this formulation gives a very clear and geometric picture of their properties.

16. Natural Operations In Differential Geometry Natural operations in differential geometry. First it should be a monographicalwork on natural bundles and natural operators in differential geometry. http://www.emis.de/monographs/KSM/

The Electronic Library of Mathematics Mathematical Monographs For fastest access: Choose your nearest mirror site! Natural operations in differential geometry by Ivan Kolar, Jan Slovak and Peter W. Michor Paper version originally published by Springer-Verlag, Berlin, Heidelberg, New York, 1993 ISBN 3-540-56235-4 (Germany) Download the whole book as one file: HYPER-DVI ] (838,207 bytes) Postscript ] (1,330,587 bytes) PDF ] (2,945,143 bytes) The aim of this book is threefold: First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. Even though Ehresmann in his original papers from 1951 underlined the conceptual meaning of the notion of an $r$-jet for differential geometry, jets have been mostly used as a purely technical tool in certain problems in the theory of systems of partial differential equations, in singularity theory, in variational calculus and in higher order mechanics. But the theory of natural bundles and natural operators clarifies once again that jets are one of the fundamental concepts in differential geometry, so that a thorough treatment of their basic properties plays an important role in this book. We also demonstrate that the central concepts from the theory of connections can very conveniently be formulated in terms of jets, and that this formulation gives a very clear and geometric picture of their properties.

17. EMIS ELibEMS: Mathematical Conference Proceedings Proceedings of the. 6th International Conference on. differential geometry andApplications. Brno, Czech Republic August 28 September 1, 1995. Editors. http://www.emis.de/proceedings/6ICDGA/

The Electronic Library of Mathematics Mathematical Conference Proceedings Proceedings of the 6th International Conference on Differential Geometry and Applications Brno, Czech Republic August 28 - September 1, 1995 Editors J. Janyska, I. Kolár and J. Slovák For fastest access: Choose your nearest server! Contents (Point to Abs to get an abstract, point to DVI to get a DVI file, point to PS to get a PostScript file.) Preface List of participants Contents (ASCII file) Part I. RIEMANNIAN GEOMETRY Part II. JETS AND NATURAL OPERATORS Part III. FURTHER GEOMETRIC STRUCTURES Part IV. ANALYSIS ON MANIFOLDS ... Part V. GEOMETRIC METHODS IN MATHEMATICAL PHYSICS Hardcopies of the Proceedings are available from Departments of Mathematics, Janáckovo nám. 2a, 662 95 Brno, Czech Republic Published by Masaryk University Brno, Czech Republic. Please, send comments and suggestions to janyska@math.muni.cz

18. EDGE A TMR network. Structure, activities, news and resources.Category Science Math Research Specialist Groups...... EUROPEAN differential geometry ENDEAVOUR. EDGE aims to encourage andfacilitate research and training in major areas of differential http://edge.imada.sdu.dk/

EDGE EDGE information Welcome Structure Activities Positions available ... About this homepage EUROPEAN DIFFERENTIAL GEOMETRY ENDEAVOUR EDGE aims to encourage and facilitate research and training in major areas of differential geometry, which is a vibrant and central topic in pure mathematics today. A significant theme which unites the areas that are the subject of this endeavour is the interface with other disciplines, both pure (topology, algebraic geometry) and applied (mathematical physics, especially gauge theory and string theory). The members of EDGE are geometers in mathematical centres spreading among most European countries. These centres are grouped into nine geographical nodes which are responsible for the management of joint research projects and for the training of young researchers through exchange between the EDGE groups. The following are some of the common mathematical themes that underlie and unify the tasks to be addressed by EDGE. Another unifying theme is the use of analytical and differential-geometric methods in attacking problems whose origin is not in differential geometry per se. These methods will be used by researchers throughout the network to investigate a wide variety of problems in related areas of mathematics including topology, algebraic geometry, and mathematical physics. In algebraic geometry, for example, there are a number of problems that are best attacked with `transcendental methods'. In some cases, the research concerns correspondences between differential-geometric and algebraic-geometric objects (as in the Hitchin-Kobayashi correspondence and its generalizations).

19. Differential Geometry And Its Applications Contact information, instructions to authors.Category Science Math Geometry Journals...... The journal publishes original research papers and survey papers in differentialgeometry and in all interdisciplinary areas in mathematics which use http://jdga.slu.cz/

Editorial Office Editor-in-Chief: O. Kowalski , Faculty of Mathematics and Physics, Charles University, Sokolovsk‡ 83, 18675 Prague 8, Czech Republic, e-mail: kowalski@karlin.mff.cuni.cz (Electronic submission of papers: dga@karlin.mff.cuni.cz Editorial board: D.V. Alekseevsky , University of Hull, Department of Mathematics, Cottingham Road, Hull HU6 7RX, U.K., D.V.Alekseevsky@maths.hull.ac.uk R. Bott , Department of Mathematics, Science Center, 1 Oxford Street, Cambridge, MA 02138, USA, bott@abel.math.harvard.edu J.-P. Bourguignon jpb@ihes.fr jpb@orphee.polytechnique.fr E-mails with attachments should be sent to the address jasserand@ihes.fr R.L. Bryant , Duke Department of Mathematics, P.O. Box 90320, Durham, NC 27708-0320 USA, bryant@math.duke.edu B.A. Dubrovin , Department of Higher Geometry and Topology, Moscow State University, 119899 Moscow, Russia, dubrovin@sissa.it M.G. Eastwood , Department of Pure Mathematics, Adelaide University, SA 5005, Australia, meastwoo@maths.adelaide.edu.au Y. Eliashberg , Department of Mathematics, Stanford University, Stanford, CA 94305, USA, eliash@math.stanford.edu

20. Bibliographies Journal of differential geometry. Access to the JDG bibliography. Journal ofdifferential geometry (WAIS); Journal of differential geometry (Glimpse). http://www.math.ufl.edu/math/biblio.html

Bibliographies We are still developing this service. Please send comments and error reports to cws@math.ufl.edu. This file was last modified on September 16, 1997 Table of Contents Introduction More about WAIS More about Glimpse Bibliography on ergodic theory and dynamical systems ... UF Math Department Home Page Introduction to the Bibliographies This is a collection of bibliographies served to the Internet by the University of Florida Department of Mathematics. Details on individual bibliographies are contained in appropriate sections below. At this writing, we offer two distinct search mechanisms for the bibliographies, which are also described in more detail below. This introduction says a bit about the two database servers and offers some general remarks on their use. Saving Your Search You probably want to save your search results to one or more files on your own computer, and most Web readers will let you do this from a Save, Save As, or Print command. Users of graphics-based browsers probably want to look for a Save As button or menu item. Lynx users would use the

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