Differential geometry : with applications to mechanics and physics
著者
書誌事項
Differential geometry : with applications to mechanics and physics
（Monographs and textbooks in pure and applied mathematics, 237）
Marcel Dekker, c2001
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注記
Includes bibliographical references (p. 443-444) and index
内容説明・目次
内容説明
An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
目次
- Part 1 Topology and differential calculus requirements: topology
- differential calculus in Banach spaces
- exercises. Part 2 Manifolds: introduction
- differential manifolds
- differential mappings
- submanifolds
- exercises. Part 3 Tangent vector space: tangent vector
- tangent space
- differential at a point
- exercises. Part 4 Tangent bundle-vector field-one-parameter group lie algebra: introduction
- tangent bundle
- vector field on manifold
- lie algebra structure
- one-parameter group of diffeomorphisms
- exercises. Part 5 Cotangent bundle-vector bundle of tensors: cotangent bundle and covector field
- tensor algebra
- exercises. Part 6 Exterior differential forms: exterior form at a point
- differential forms on a manifold
- pull-back of a differential form
- exterior differentiation
- orientable manifolds
- exercises. Part 7 Lie derivative-lie group: lie derivative
- inner product and lie derivative
- Frobenius theorem
- exterior differential systems
- invariance of tensor fields
- lie group and algebra
- exercises. Part 8 Integration of forms: n-form integration on n-manifold
- integral over a chain
- Stokes' theorem
- an introduction to cohomology theory
- integral invariants
- exercises. Part 9 Riemann geometry: Riemannian manifolds.
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