Geometry VI [electronic resource] Riemannian Geometry / by M.M. Postnikov.

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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-...

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Bibliographic Details
Uniform Title:Encyclopaedia of Mathematical Sciences ; 91
Main Author: Postnikov, M.M (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
Edition:1st ed. 2001.
Series:Encyclopaedia of Mathematical Sciences ; 91
Subjects:
Geometry.
Geometry, Differential.
Online Access:
Springer Book Archive - Mathematics: 2001 (Springer Link)
Variant Title:
Geometry VI: Riemannian Geometry
Format: Electronic eBook
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.