Tensors and Manifolds
With Applications to Mechanics and Relativity
Published on 30. July 1992
Book
Hardback
424 pages
978-0-19-506561-9 (ISBN)
Description
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.
Reviews / Votes
[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 ReviewsMore details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Illustrations
fig.
line figures
ISBN-13
978-0-19-506561-9 (9780195065619)
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Schweitzer Classification
Content
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.