UID:
edocfu_9959245416902883
Umfang:
1 online resource (420 p.)
Ausgabe:
2nd rev. ed.
ISBN:
3-11-090512-4
Serie:
De Gruyter studies in mathematics ;
Inhalt:
Riemannian Geometry (Degruyter Studies in Mathematics)
Anmerkung:
Description based upon print version of record.
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Front matter --
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Chapter 1: Foundations. --
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1.0 Review of Differential Calculus and Topology --
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1.1 Differentiable Manifolds --
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1.2 Tensor Bundles --
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1.3 Immersions and Submersions --
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1.4 Vector Fields and Tensor Fields --
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1.5 Covariant Derivation --
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1.6 The Exponential Mapping --
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1.7 Lie Groups --
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1.8 Riemannian Manifolds --
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1.9 Geodesics and Convex Neighborhoods --
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1.10 Isometric Immersions --
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1.11 Riemannian Curvature --
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1.12 Jacobi Fields --
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Chapter 2: Curvature and Topology. --
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2.1 Completeness and Cut Locus --
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2.1 Appendix - Orientation --
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2.2 Symmetric Spaces --
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2.3 The Hilbert Manifold of H1-curves --
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2.4 The Loop Space and the Space of Closed Curves --
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2.5 The Second Order Neighborhood of a Critical Point --
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2.5 Appendix - The S1- and the Ζ2-action on AM --
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2.6 Index and Curvature --
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2.6 Appendix - The Injectivity Radius for 1/4-pinched Manifolds --
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2.7 Comparison Theorems for Triangles --
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2.8 The Sphere Theorem --
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2.9 Non-compact Manifolds of Positive Curvature --
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Chapter 3: Structure of the Geodesic Flow. --
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3.1 Hamiltonian Systems --
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3.2 Properties of the Geodesic Flow --
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3.3 Stable and Unstable Motions --
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3.4 Geodesics on Surfaces --
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3.5 Geodesics on the Ellipsoid --
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3.6 Closed Geodesies on Spheres --
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3.7 The Theorem of the Three Closed Geodesics --
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3.8 Manifolds of Non-Positive Curvature --
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3.9 The Geodesic Flow on Manifolds of Negative Curvature --
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3.10 The Main Theorem for Surfaces of Genus 0 --
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References --
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Index
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Issued also in print.
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English
Weitere Ausg.:
ISBN 3-11-014593-6
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783110905120
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