| Description |
1 online resource (420 pages) |
| Series |
De Gruyter Studies in Mathematics ; v. 1 |
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De Gruyter studies in mathematics.
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| 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 |
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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 |
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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 |
| Summary |
Riemannian Geometry (Degruyter Studies in Mathematics) |
| Bibliography |
Includes bibliographical references (p. [393]-402) and index |
| Notes |
English |
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Print version record |
| Subject |
Geometry, Riemannian.
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Geometry, Differential.
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Geometry, Differential
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Geometry, Riemannian
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| Form |
Electronic book
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| LC no. |
95002589 |
| ISBN |
9783110905120 |
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3110905124 |
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