Author | Gallot, Sylvestre. author |
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Title | Riemannian Geometry [electronic resource] / by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1990 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-97242-3 |
Descript | XIII, 286 p. online resource |
I. Differential Manifolds -- A. From Submanifolds to Abstract Manifolds -- B. Tangent Bundle -- C. Vector Fields -- D. Baby Lie Groups -- E. Covering Maps and Fibrations -- F. Tensors -- A characterization for tensors -- G. Exterior Forms -- H. Appendix: Partitions of Unity -- II. Riemannian Metrics -- A. Existence Theorems and First Examples -- B. Covariant Derivative -- C. Geodesics -- Definitions -- III. Curvature -- A. The Curvature Tensor -- B. First and Second Variation of Arc-Length and Energy -- C. Jacobi Vector Fields -- E. The Behavior of Length and Energy in the Neighborhood of a Geodesic -- F. Manifolds with Constant Sectional Curvature -- G. Topology and Curvature -- H. Curvature and Volume -- I. Curvature and Growth of the Fundamental Group -- J. Curvature and Topology: An Account of Some Old and Recent Results -- K. Curvature Tensors and Representations of the Orthogonal Group -- L. Hyperbolic Geometry -- M. Conformai Geometry -- IV. Analysis on Manifolds and the Ricci Curvature -- A. Manifolds with Boundary -- B. Bishopโs Inequality Revisited -- C. Differential Forms and Cohomology -- A second visit to the Bochner method -- D. Basic Spectral Geometry -- E. Some Examples of Spectra -- F. The Minimax Principle -- G. The Ricci Curvature and Eigenvalues Estimates -- H. Paul Levyโs Isoperimetric Inequality -- V. Riemannian Submanifolds -- A. Curvature of Submanifolds -- B. Curvature and Convexity -- C. Minimal Surfaces -- Some Extra Problems -- Solutions of Exercises -- I -- II -- III -- IV -- V