Author(s): Wilhelm P. A. Klingenberg
Edition: 2
Publisher: Walter de Gruyter
Year: 1995
Title page
Prefaces
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 Geodesies 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 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 Geodesics 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
