Riemannian geometry [[electronic resource] /] / Wilhelm P.A. Klingenberg

• Autore: Klingenberg Wilhelm <1924-2010.>
• Pubblicazione: Berlin ; ; New York, : W. de Gruyter, 1995
• Edizione: 2nd rev. ed.
• Descrizione fisica: 1 online resource (420 p.)
• Disciplina: 516.3/73
• Soggetto topico: Geometry, Riemannian; Geometry, Differential
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [393]-402) and index.
• Nota di contenuto: Front matter -- 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
• Sommario/riassunto: Riemannian Geometry (Degruyter Studies in Mathematics)
• Titolo autorizzato: Riemannian geometry
• ISBN: 3-11-090512-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910462028403321
• Lo trovi qui: Univ. Federico II
• Serie: De Gruyter Studies in Mathematics