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  3. Applicable Differential Geometry
  • Cited by 28
Publisher:
Cambridge University Press
Online publication date:
August 2012
Print publication year:
1987
Online ISBN:
9780511623905
DOI:
https://doi.org/10.1017/CBO9780511623905
Subjects:
Mathematics (general), Mathematics, Mathematical Physics, Geometry and Topology
Series:
London Mathematical Society Lecture Note Series (59)
Information

Book description

This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.

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