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Riemannian Geometry
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Wilhelm P.A. Klingenberg
Language:
English
Published/Copyright:
1995
Reviews
"Perhaps it could best be described as an excellent monograph on geodesics which has been expanded to include an introduction to the preliminary ideas which this requires. [...] The main subject of this book is exciting and new results are constantly being obtained. Any differential geometer should know something about geodesics and this is a good place to read about it, as well as to find many useful ideas and examples for reference." Mathematical Reviews (review of the first edition)
"Now in its second edition, this textbook continuous to offer the probably best introduction to the topics in Riemannian geometry which are centred around the theory of geodesics." Zentralblatt für Mathematik
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Frontmatter
I - 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
13 -
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1.3 Immersions and Submersions
23 -
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1.4 Vector Fields and Tensor Fields
31 -
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1.5 Covariant Derivation
39 -
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1.6 The Exponential Mapping
53 -
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1.7 Lie Groups
59 -
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1.8 Riemannian Manifolds
67 -
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1.9 Geodesics and Convex Neighborhoods
78 -
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1.10 Isometric Immersions
86 -
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1.11 Riemannian Curvature
97 -
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1.12 Jacobi Fields
109 - Chapter 2: Curvature and Topology.
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2.1 Completeness and Cut Locus
124 -
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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
158 -
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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
181 -
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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
240 - Chapter 3: Structure of the Geodesic Flow.
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3.1 Hamiltonian Systems
256 -
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3.2 Properties of the Geodesic Flow
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3.3 Stable and Unstable Motions
279 -
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3.4 Geodesics on Surfaces
288 -
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3.5 Geodesics on the Ellipsoid
303 -
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3.6 Closed Geodesies on Spheres
324 -
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3.7 The Theorem of the Three Closed Geodesics
337 -
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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
393 -
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Index
403
Publishing information
Pages and Images/Illustrations in book
eBook published on:
May 3, 2011
eBook ISBN:
9783110905120
Hardcover published on:
April 6, 1995
Hardcover ISBN:
9783110145939
Edition:
2. rev. ed.
Pages and Images/Illustrations in book
Front matter:
10
Main content:
409
Keywords for this book
Riemannsche Geometrie
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Walter de Gruyter GmbH
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