Abstract
The theory of manifolds is basic for the theory of Lie groups and Riemannian and Einsteinian geometries. The introduction of the manifold concept into general relativity around 1960, mainly by Martin Kruskal, put a new light on that subject and clarified the topological properties, both local and global, of space-time models. Statistical mechanics deals with flows on manifolds. Other applications of manifolds to physics appear from time to time, because of their basic geometric nature. Only finite-dimensional manifolds will be discussed. For more general manifolds, see Lang 1962.
Prerequisites: Chapters 18 and 19.
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© 1981 Springer-Verlag Inc.
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Richtmyer, R.D. (1981). Elementary Theory of Manifolds. In: Principles of Advanced Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51076-2_6
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DOI: https://doi.org/10.1007/978-3-642-51076-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-51078-6
Online ISBN: 978-3-642-51076-2
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