Lectures on Differential Geometry

by Chern, Shiing-Shen; Chen, W. H.; Lam, K. S.

• ISBN13: 9789810241827
• ISBN10: 9810241828
• Format: Paperback
• Copyright: 1999-11-01
• Publisher: World Scientific Pub Co Inc

Summary

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, beth prepared specially for this edition by Professor Chern to bring the text up-to-date.

Table of Contents

Differentiable Manifolds	p. 1
Multilinear Algebra	p. 39
Exterior Differential Calculus	p. 65
Connections	p. 101
Riemannian Geometry	p. 133
Lie Groups and Moving Frames	p. 173
Complex Manifolds	p. 221
Finsler Geometry	p. 265
A: Historical Notes	p. 331
Differential Geometry and Theoretical Physics	p. 335
References	p. 343
Index	p. 347
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