Kooperativer Bibliotheksverbund

UID:

Format: 1 online resource (419p.)

Edition: 2. rev. ed.

ISBN: 9783110905120

Series Statement: De Gruyter Studies in Mathematics, 1

Note: 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 , In English.

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110905120

URL: https://doi.org/10.1515/9783110905120

URL: https://doi.org/10.1515/9783110905120

URL: https://www.degruyter.com/isbn/9783110905120

URL: Cover

UID:

Format: Online-Ressource (x, 409 p)

Edition: 2nd rev. ed

Edition: 2011

ISBN: 9783110905120

Series Statement: De Gruyter Studies in Mathematics 1

Content: Riemannian Geometry (Degruyter Studies in Mathematics)

Note: In English

Additional Edition: ISBN 3110145936

Additional Edition: ISBN 9783110145939

Additional Edition: ISBN 9783110905120

Additional Edition: Erscheint auch als Druck-Ausgabe Klingenberg, Wilhelm, 1924 - 2010 Riemannian geometry Berlin : W. de Gruyter, 1995 ISBN 3110145936

Language: English

Subjects: Mathematics

Keywords: Riemannsche Geometrie

DOI: 10.1515/9783110905120

URL: Volltext

URL: Volltext  (lizenzpflichtig)

URL: lizenzpflichtig

URL: Cover

URL: Cover

Author information: Klingenberg, Wilhelm 1924-2010

UID:

Format: 1 online resource (419p.)

Edition: 2. rev. ed.

ISBN: 9783110905120

Series Statement: De Gruyter Studies in Mathematics, 1

Note: 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 , In English.

Language: English

DOI: 10.1515/9783110905120

URL: https://doi.org/10.1515/9783110905120

UID:

Format: 1 Online-Ressource

Edition: 2., rev. ed., originally published 1995

ISBN: 9783110905120

Series Statement: De Gruyter studies in mathematics 1

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 3-11-014593-6

Language: English

Subjects: Mathematics

Keywords: Riemannsche Geometrie

DOI: 10.1515/9783110905120

URL: Volltext  (URL des Erstveröffentlichers)

Author information: Klingenberg, Wilhelm 1924-2010

UID:

Format: 1 online resource (420 p.)

Edition: 2nd rev. ed.

ISBN: 3-11-090512-4

Series Statement: De Gruyter studies in mathematics ;

Content: Riemannian Geometry (Degruyter Studies in Mathematics)

Note: Description based upon print version of record. , 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 , Issued also in print. , English

Additional Edition: ISBN 3-11-014593-6

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110905120

UID:

Format: Online-Ressource (x, 409 p) , ill

Edition: 2nd rev. ed

Edition: Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web

ISBN: 3110145936 (acid-free paper) , 9783110145939 (acid-free paper) , 9783110905120

Series Statement: De Gruyter studies in mathematics 1

Content: Riemannian Geometry (Degruyter Studies in Mathematics)

Note: Includes bibliographical references (p. [393]-402) and index , 2.4 The Loop Space and the Space of Closed Curves2.5 The Second Order Neighborhood of a Critical Point; 2.5 Appendix - The S1- and the Z2-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 Geodesics3.8 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. , 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.

Language: English

DOI: 10.1515/9783110905120

URL: http://www.degruyter.com/doi/book/10.1515/9783110905120

URL: Cover