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Lectures on Differential Geometry(2000)
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S.S Chern & S.S Chen & K.S Lam
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World Scientific
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1 edition
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368 pages
ISBN
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9810241828
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25,000¿ø
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750 Point
This is a translation of an 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, sought to combine 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 fibre 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 specifically for this edition by Professor Chern to bring the text into perspective.
1.Differentiable Manifolds
2.Multilinear algebra
3.Exterior differential calculus
4.Connections
5.Riemannian geometry
6.Lie groups and moving frames
7.Complex manifolds
8.Finsler geometry
"Let me begin by saying that I am biased. I worked as Mr. Chern's assistant in a differential geometry class when I was a grad student. He was a great person to work for and his lectures were well organized. This book is a NOT aimed at the typical undergraduate. It is a major advance in comprehensability from the books from which I learned the covered material. Modern differential geometry does not yet have a great, easy for the novice, self-study friendly text that really covers the material - this book and the Russian trilogy by Dubrovin, et al. are major steps along the way."
"I read the Chinese version of this book published by Peking University Press some time ago. Now, I am inpatiently waiting for the English version. It has been delayed again and again. This book is very concised and not suitable for beginners who want to learn the subject by this book. Wu's Chinese book of "Rieman Geometry" is a more friendly book dealing on the introductory level. Nevertheless, I like Chern's book a lot. It comes handy to review the subject. If you are an advanced reader, you will find this book to be very enjoyable like me."
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