Riemannian Manifolds
Title | Riemannian Manifolds PDF eBook |
Author | John M. Lee |
Publisher | Springer Science & Business Media |
Pages | 232 |
Release | 2006-04-06 |
Genre | Mathematics |
ISBN | 0387227261 |
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Introduction to Riemannian Manifolds
Title | Introduction to Riemannian Manifolds PDF eBook |
Author | John M. Lee |
Publisher | Springer |
Pages | 437 |
Release | 2019-01-02 |
Genre | Mathematics |
ISBN | 3319917552 |
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Curvature and Topology of Riemannian Manifolds
Title | Curvature and Topology of Riemannian Manifolds PDF eBook |
Author | Katsuhiro Shiohama |
Publisher | Springer |
Pages | 343 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540388273 |
Curvature and Homology
Title | Curvature and Homology PDF eBook |
Author | Samuel I. Goldberg |
Publisher | Courier Corporation |
Pages | 417 |
Release | 1998-01-01 |
Genre | Mathematics |
ISBN | 048640207X |
This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian manifolds. Includes four helpful appendixes. "A valuable survey." — Nature. 1962 edition.
Global Riemannian Geometry: Curvature and Topology
Title | Global Riemannian Geometry: Curvature and Topology PDF eBook |
Author | Ana Hurtado |
Publisher | Springer Nature |
Pages | 121 |
Release | 2020-08-19 |
Genre | Mathematics |
ISBN | 3030552934 |
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
Curvature and Topology of Riemannian Manifolds
Title | Curvature and Topology of Riemannian Manifolds PDF eBook |
Author | Katsuhiro Shiohama |
Publisher | |
Pages | 348 |
Release | 2014-01-15 |
Genre | |
ISBN | 9783662190036 |
Riemannian Topology and Geometric Structures on Manifolds
Title | Riemannian Topology and Geometric Structures on Manifolds PDF eBook |
Author | Krzysztof Galicki |
Publisher | Springer Science & Business Media |
Pages | 303 |
Release | 2010-07-25 |
Genre | Mathematics |
ISBN | 0817647430 |
Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.