03458nam 2200649Ia 450 991046202840332120211202202837.03-11-090512-410.1515/9783110905120(CKB)2670000000250817(EBL)936428(OCoLC)843635427(SSID)ssj0000560176(PQKBManifestationID)11342024(PQKBTitleCode)TC0000560176(PQKBWorkID)10568730(PQKB)11742925(MiAaPQ)EBC936428(WaSeSS)Ind00013381(DE-B1597)40789(OCoLC)979762977(DE-B1597)9783110905120(PPN)175577269(Au-PeEL)EBL936428(CaPaEBR)ebr10597530(EXLCZ)99267000000025081719950110d1995 uy 0engurnn#---|u||utxtccrRiemannian geometry[electronic resource] /Wilhelm P.A. Klingenberg2nd rev. ed.Berlin ;New York W. de Gruyter19951 online resource (420 p.)De Gruyter Studies in Mathematics ;1Description based upon print version of record.3-11-014593-6 Includes bibliographical references (p. [393]-402) and index.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 --IndexRiemannian Geometry (Degruyter Studies in Mathematics)De Gruyter Studies in MathematicsGeometry, RiemannianGeometry, DifferentialElectronic books.Geometry, Riemannian.Geometry, Differential.516.3/73Klingenberg Wilhelm1924-2010.42056MiAaPQMiAaPQMiAaPQBOOK9910462028403321Riemannian geometry45718UNINA