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Geometry. / VI, Riemannian geometry

Author: Mihail Mihailovič Postnikov; Sergei Andreevich Vakhromeev
Publisher: Berlin ; Heidelberg ; New York : Springer, cop. 2001.
Series: Encyclopaedia of mathematical sciences, 91.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. The author successfully combines the co-ordinate and invariant approaches  Read more...

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Document Type: Book
All Authors / Contributors: Mihail Mihailovič Postnikov; Sergei Andreevich Vakhromeev
ISBN: 3540411089 9783540411086
OCLC Number: 492890468
Notes: Traducteur d'après les p. liminaires.
Trad. de : "Rimanova geometriya" publié en 1998.
Description: 1 vol. (XVIII-503 p.) : ill. ; 24 cm.
Contents: 1. Affine Connections.- 2. Covariant Differentiation. Curvature.- 3. Affine Mappings. Submanifolds.- 4. Structural Equations. Local Symmetries.- 5. Symmetric Spaces.- 6. Connections on Lie Groups.- 7. Lie Functor.- 8. Affine Fields and Related Topics.- 9. Cartan Theorem.- 10. Palais and Kobayashi Theorems.- 11. Lagrangians in Riemannian Spaces.- 12. Metric Properties of Geodesics.- 13. Harmonic Functionals and Related Topics.- 14. Minimal Surfaces.- 15. Curvature in Riemannian Space.- 16. Gaussian Curvature.- 17. Some Special Tensors.- 18. Surfaces with Conformal Structure.- 19. Mappings and Submanifolds I.- 20. Submanifolds II.- 21. Fundamental Forms of a Hypersurface.- 22. Spaces of Constant Curvature.- 23. Space Forms.- 24. Four-Dimensional Manifolds.- 25. Metrics on a Lie Group I.- 26. Metrics on a Lie Group II.- 27. Jacobi Theory.- 28. Some Additional Theorems I.- 29. Some Additional Theorems II.- Addendum.- 30. Smooth Manifolds.- 31. Tangent Vectors.- 32. Submanifolds of a Smooth Manifold.- 33. Vector and Tensor Fields. Differential Forms.- 34. Vector Bundles.- 35. Connections on Vector Bundles.- 36. Curvature Tensor.- Bianchi Identity.- Suggested Reading.
Series Title: Encyclopaedia of mathematical sciences, 91.
Other Titles: Rimanova geometriya
Riemannian geometry
Responsibility: M.M. Postnikov ; [trad. du russe par S.A. Vakhrameev ...].
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From the reviews of the first edition:"... The book is .. comprehensive and original enough to be of interest to any professional geometer, but I particularly recommend it to the advanced student, Read more...

 
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