Title: Riemannian geometry /
Authors: Willmore, T. 1919-
Publisher: Clarendon Press ; Oxford University Press,
Year: 1993
Subjects: Geometry, Riemannian.
Contents: 1. Differentiable manifolds -- 1.1. Preliminaries -- 1.2. Differentiable manifolds -- 1.3. Tangent vectors -- 1.4. The differential of a map -- 1.5. The tangent and cotangent bundles -- 1.6. Submanifolds; the inverse and implicit function theorems -- 1.7. Vector fields -- 1.8. Distributions -- 2. Tensors and differential forms -- 2.1. Tensor product -- 2.2. Tensor fields and differential forms -- 2.3. Exterior derivation -- 2.4. Differential ideals and the theorem of Frobenius -- 2.5. Orientation of manifolds -- 2.6. Covariant differentiation -- 2.7. Identities satisfied by the curvature and torsion tensors -- 2.8. The Koszul connexion -- 2.9. Connexions and moving frames -- 2.10. Tensorial forms -- 3. Riemannian manifolds -- 3.1. Riemannian metrics -- 3.2. Identities satisfied by the curvature tensor of a Riemannian manifold -- 3.3. Sectional curvature -- 3.4. Geodesics -- 3.5. Normal coordinates -- 3.6. Volume form -- 3.7. The Lie derivative -- 3.8. The Hodge star operator --^