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What is Riemannian Geometry (Oxford Science Publications) about?

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 --^ 3.9. Maxwell's Equations -- 3.10. Consequences Of The Theorems Of Stokes And Of Hodge -- 3.11. The Space Of Curvature Tensors -- 3.12. Conformal Metrics And Conformal Connexions -- 4. Submanifold Theory --

Author

Willmore, T. J.

Publisher

Oxford, Eng.: Clarendon Press ; New York: Oxford University Press

Published

1993

Language

EN

ISBN

9780198532538

Subjects

Mathematics, Stem