Tensors and Manifolds: With Applications to Mechanics and Relativity - Rilegato

Wasserman, Robert H.

9780195065619: Tensors and Manifolds: With Applications to Mechanics and Relativity

Rilegato

ISBN 10: 0195065611 ISBN 13: 9780195065619

Casa editrice: OUP USA, 1992

This book introduces the concepts of tensor algebras and differentiable manifolds. It describes analytical and geometrical structures built on these basic concepts. Those structures - which include differential forms and their integration, flows, Lie derivatives, distributions and their integrability conditions, connections, and pseudo-Riemannian and symplectic manifolds - are then applied to the description of the fundamental ideas and Hamiltonian and Lagrangian mechanics, and special and general relativity. This book is designed to be accessible to the mathematics or physics student with a good standard undergraduate background, who is interested in obtaining a broader perspective of the rich interplay of mathematics and physics before deciding on a specialty.

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Recensione:

[A] nice and comprehensive introduction... The book is clearly written and self-contained and, in particular, the author has succeeded in combining mathematical rigor with a certain degree of informality... this work will certainly be appreciated by a wide audience. (Frans Cantrijn, Mathematical Reviews)

Contenuti:

Vector spaces; Multilinear mappings and dual spaces; Tensor product spaces; Tensors; Symmetric and skew-symmetric tensors; Exterior (Grassman) algebra; The tangent map of real cartesian spaces; Topological spaces; Differentiable manifolds; Submanifolds; Vector fields, 1-forms, and other tensor fields; Exterior differentiation and integration of differential forms; The flow, and the lie derivative of a vector field; Integrability conditions for distributions of a vector field; Integrability conditions for distributions and for Pfaffian systems; Pseudo-riemannian geometry; Connection 1-forms; Connections on manifolds; Mechanics; Additional topics in mechanics; A spacetime; Some physics on Minkowski spacetime; Einstein spacetimes; Spacetimes near an isolated star; Nonempty spacetimes.

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