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Geometry VI

Riemannian Geometry

  • M. M. Postnikov

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 91)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. M. M. Postnikov
    Pages 1-13
  3. M. M. Postnikov
    Pages 14-28
  4. M. M. Postnikov
    Pages 29-43
  5. M. M. Postnikov
    Pages 44-54
  6. M. M. Postnikov
    Pages 55-66
  7. M. M. Postnikov
    Pages 67-76
  8. M. M. Postnikov
    Pages 77-86
  9. M. M. Postnikov
    Pages 87-100
  10. M. M. Postnikov
    Pages 101-113
  11. M. M. Postnikov
    Pages 114-126
  12. M. M. Postnikov
    Pages 127-140
  13. M. M. Postnikov
    Pages 141-158
  14. M. M. Postnikov
    Pages 159-175
  15. M. M. Postnikov
    Pages 176-192
  16. M. M. Postnikov
    Pages 193-206
  17. M. M. Postnikov
    Pages 207-222
  18. M. M. Postnikov
    Pages 223-237
  19. M. M. Postnikov
    Pages 238-247
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    Pages 248-261
  21. M. M. Postnikov
    Pages 262-275
  22. M. M. Postnikov
    Pages 276-287
  23. M. M. Postnikov
    Pages 288-297
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    Pages 298-307
  25. M. M. Postnikov
    Pages 308-323
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    Pages 324-332
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    Pages 333-343
  28. M. M. Postnikov
    Pages 344-359
  29. M. M. Postnikov
    Pages 360-370
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    Pages 371-380
  31. M. M. Postnikov
    Pages 381-381
  32. M. M. Postnikov
    Pages 381-393
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    Pages 394-403
  34. M. M. Postnikov
    Pages 404-412
  35. M. M. Postnikov
    Pages 413-435
  36. M. M. Postnikov
    Pages 436-453
  37. M. M. Postnikov
    Pages 454-474
  38. M. M. Postnikov
    Pages 475-493
  39. Back Matter
    Pages 494-503

About this book

Introduction

This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. Before going to Riemannian geometry, the author pre- sents a more general theory of manifolds with a linear con- nection. Having in mind different generalizations of Rieman- nian manifolds, it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature. Much attention is paid to trans- formation groups of smooth manifolds. Throughout the book, different aspects of symmetric spaces are treated. The author successfully combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject.The book contains a very useful large Appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources. The results are well presented and useful for students in mathematics and theoretical physics, and for experts in these fields. The book can serve as a textbook for students doing geometry, as well as a reference book for professional mathematicians and physicists.

Keywords

Lie groups Minimal surface Riemannian geometry connections differential geometry manifold symmetric spaces

Authors and affiliations

  • M. M. Postnikov
    • 1
  1. 1.MIRANMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04433-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07434-9
  • Online ISBN 978-3-662-04433-9
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site