Riemannian Geometry
Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianch...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1987, 1987
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| Edition: | 1st ed. 1987 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I: Differential Manifolds
- A. from Submanifolds to Abstract Manifolds
- B. Tangent Bundle
- C. Vector Fields:
- D. Baby lie Groups
- E. Covering maps and Fibrations
- F. Tensors
- G. Exterior forms
- H. Appendix: Partitions of Unity
- II: Riemannian Metrics
- A. Existence Theorems and first Examples
- B. Covariant Derivative
- C. Geodesics
- III: Curvature
- A. the Curvature Tensor
- B. first Second Variation of arc-Length and Energy
- C. Jacobi Vector Fields
- D. Riemannian Submersions and Curvature
- E. The Behavior of Length and Energy in the Neighborhood of a Geodesic
- F. Manifolds with Constant Sectional Curvature
- G. Topology and Curvature
- H. Curvature and Volume
- I. Curvature and Growth of the Fundamental Group
- J. Curvature and Topology
- K. Curvature and Representations of the Orthogonal Group
- Chapitre IV: Analysis on Manifolds and the Ricci Curvature
- A. Manifolds with Boundary
- B. Bishop’s Inequality Revisited
- C. Differential forms and Cohomology
- D. Basic Spectral Geometry
- E. Some Examples of Spectra
- F. The Minimax Principle
- V. Riemannian Submanifolds