Riemannian Geometry / / Wilhelm P.A. Klingenberg.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Klingenberg, Wilhelm P.A.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©1995
• Year of Publication: 2011
• Edition: 2. rev. ed.
• Language: English
• Series: De Gruyter Studies in Mathematics , 1
• Physical Description: 1 online resource (409 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110905120; 9783110494938; 9783110637199; 9783110233957
• ISSN: 0179-0986
• DOI: 10.1515/9783110905120
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Wilhelm P.A. Klingenberg.