Riemannian Geometry.
Riemannian Geometry (Degruyter Studies in Mathematics).
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| Online Access: |
Full text (MCPHS users only) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin :
De Gruyter,
1995
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| Edition: | 2nd ed. |
| Series: | De Gruyter studies in mathematics.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- Chapter 1: Foundations; 1.0 Review of Differential Calculus and Topology; 1.1 Differentiable Manifolds; 1.2 Tensor Bundles; 1.3 Immersions and Submersions; 1.4 Vector Fields and Tensor Fields; 1.5 Covariant Derivation; 1.6 The Exponential Mapping; 1.7 Lie Groups; 1.8 Riemannian Manifolds; 1.9 Geodesics and Convex Neighborhoods; 1.10 Isometric Immersions; 1.11 Riemannian Curvature; 1.12 Jacobi Fields; Chapter 2: Curvature and Topology; 2.1 Completeness and Cut Locus; 2.1 Appendix
- Orientation; 2.2 Symmetric Spaces; 2.3 The Hilbert Manifold of H1-curves
- 2.4 The Loop Space and the Space of Closed Curves2.5 The Second Order Neighborhood of a Critical Point; 2.5 Appendix
- The S1- and the Z2-action on AM; 2.6 Index and Curvature; 2.6 Appendix
- The Injectivity Radius for 1/4-pinched Manifolds; 2.7 Comparison Theorems for Triangles; 2.8 The Sphere Theorem; 2.9 Non-compact Manifolds of Positive Curvature; Chapter 3: Structure of the Geodesic Flow; 3.1 Hamiltonian Systems; 3.2 Properties of the Geodesic Flow; 3.3 Stable and Unstable Motions; 3.4 Geodesics on Surfaces; 3.5 Geodesics on the Ellipsoid; 3.6 Closed Geodesies on Spheres
- 3.7 The Theorem of the Three Closed Geodesics3.8 Manifolds of Non-Positive Curvature; 3.9 The Geodesic Flow on Manifolds of Negative Curvature; 3.10 The Main Theorem for Surfaces of Genus 0; References; Index
