Format:
X, 409 S
,
graph. Darst
Edition:
2., rev. ed.
ISBN:
3110145936
Series Statement:
De Gruyter studies in mathematics 1
Content:
Ch. 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 -- Ch. 2. Curvature and Topology. 2.1. Completeness and Cut Locus -- 2.1. Appendix - Orientation. 2.2. Symmetric Spaces. 2.3. The Hilbert Manifold of H[superscript 1]-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 S[Superscript 1]- and the Z[subscript 2]-action on [lambda]M. 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
Note:
Literaturverz. S. [393] - 402
,
Ch. 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 -- Ch. 2. Curvature and Topology. 2.1. Completeness and Cut Locus -- 2.1. Appendix - Orientation. 2.2. Symmetric Spaces. 2.3. The Hilbert Manifold of H[superscript 1]-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 S[Superscript 1]- and the Z[subscript 2]-action on [lambda]M. 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.
Additional Edition:
Online-Ausg. Klingenberg, Wilhelm, 1924 - 2010 Riemannian Geometry Berlin ;New York : W. de Gruyter, 2011 ISBN 9783110905120
Additional Edition:
Erscheint auch als Online-Ausgabe Klingenberg, Wilhelm P. A Riemannian Geometry. Berlin/Boston : De Gruyter, Inc., 2011 ISBN 9783110905120
Language:
English
Subjects:
Mathematics
Keywords:
Riemannsche Geometrie
;
Riemannsche Geometrie
Author information:
Klingenberg, Wilhelm 1924-2010
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