Author | Petersen, Peter. author |
---|---|
Title | Riemannian Geometry [electronic resource] / by Peter Petersen |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-6434-5 |
Descript | X, 198 p. online resource |
1 Riemannian Metrics -- 2 Curvature -- 3 Examples -- 4 Hypersurfaces -- 5 Geodesics and Distance -- 6 Sectional Curvature Comparison I -- 7 The Bochner Technique -- 8 Symmetric Spaces and Holonomy -- 9 Ricci Curvature Comparison -- 10 Convergence -- 11 Sectional Curvature Comparison II -- A de Rham Cohomology -- A.1 Elementary Properties -- A.2 Integration of Forms -- A.3 ?ech Cohomology -- A.4 de Rham Cohomology -- A.5 Poincarรฉ Duality -- A.6 Degree Theory -- A.7 Further Study -- B Principal Bundles -- B.1 Cartan Formalism -- B.2 The Frame Bundle -- B.3 Construction of the Frame Bundle -- B.4 Construction of Tensor Bundles -- B.5 Tensors -- B.6 The Connection on the Frame Bundle -- B.7 Covariant Differentiation of Tensors -- B.8 Principal Bundles in General -- B.9 Further Study -- C Spinors -- C.1 Spin Structures -- C.2 Spinor Bundles -- C.3 The Weitzenbรถck Formula for Spinors -- C.4 The Square of a Spinor -- C.5 Further Study -- References