Kooperativer Bibliotheksverbund

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Format: 1 online resource (419p.)

Edition: 2. rev. ed.

ISBN: 9783110905120

Series Statement: De Gruyter Studies in Mathematics, 1

Note: Frontmatter -- , 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 Curves -- , 2.5 The Second Order Neighborhood of a Critical Point -- , 2.5 Appendix – The S1- and the Ζ2-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 Geodesics -- , 3.8 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 , In English.

Language: English

DOI: 10.1515/9783110905120

URL: https://doi.org/10.1515/9783110905120