Lectures on Differential Geometry (Series on University Mathematics, Vol. 1)
by: Shiing-Shen Chern Wei-Huan Chen K. S. Lam
About
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, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.
Contents:
* Differentiable Manifolds
* Multilinear Algebra
* Exterior Differential Calculus
* Connections
* Riemannian Geometry
* Lie Groups and Moving Frames
* Complex Manifolds
* Finsler Geometry
* Historical Notes
* Differential Geometry and Theoretical Physics
Readership: Undergraduates, graduates and researchers in pure mathematics and mathematical physics.
"This excellent and polished book may not be suitable for the very beginning student, but it is highly recommended for all mathematicians, from the advanced undergraduate student to the experienced professor. For many mathematicians it will be a work of reference for their research. It will be welcome by physicists."
Prof. F Hirzebruch
Max-Planck Institute, Bonn
"The material of this book provides a solid and comprehensive background for more advanced and specialized studies."
Mathematics Abstracts
About the Author
Professor Shiing-shen Chern retired from UC Berkeley and is now based in the Nankai Institute of Mathematics, which he founded in 1985. He is also the founding director of the Mathematical Science Research Institute, Berkeley (1981).
He was awarded the National Science Medal in 1975 and Wolf Prize in Mathematics in 1983/4. His area of research was differential geometry where he studied the (now named) Chern characteristic classes in fibre spaces.
The Chern Visiting Professorship, begun in 1996, honors the Berkeley professor emeritus widely regarded as the greatest geometer of his generation. "Chern's belief in young people and his encouragement of them had a lot to do with the spectacular growth of geometry in the second half of this century", mathematician Blaine Lawson has said. "It is not easy to find a geometer who was not for some period of time either a student or a post-doctoral fellow in the orbit of Chern".
http://ifile.it/05yfuz/chern.djvu
