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Tensors and Manifolds


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Table of Contents

1: Vector spaces
2: Multilinear mappings and dual spaces
3: Tensor product spaces
4: Tensors
5: Symmetric and skew-symmetric tensors
6: Exterior (Grassmann) algebra
7: The tangent map of real cartesian spaces
8: Topological spaces
9: Differentiable manifolds
10: Submanifolds
11: Vector fields, 1-forms and other tensor fields
12: Differentiation and integration of differential forms
13: The flow and the Lie derivative of a vector field
14: Integrability conditions for distributions and for pfaffian systems
15: Pseudo-Riemannian manifolds
16: Connection 1-forms
17: Connection on manifolds
18: Mechanics
19: Additional topics in mechanics
20: A spacetime
21: Some physics on Minkowski spacetime
22: Einstein spacetimes
23: Spacetimes near an isolated star
24: Nonempty spacetimes
25: Lie groups
26: Fiber bundles
27: Connections on fiber bundles
28: Gauge theory

About the Author

Robert H. Wasserman is Professor Emeritus of Mathematics at Michigan State University, USA.


`Review from previous edition Clearly written and self-contained and, in particular, the author has succeeded in combining mathematical rigor with a certain degree of informality in a satisfactory way. As such, this work will certainly be appreciated by a wide audience.'
Mathematical Reviews, August 1993

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