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Riemannian Geometry in an Orthogonal Frame: From Lectures Delivered by Elie Cartan at the Sorbonne in 1926-27 | 
 enlarge | Authors: Elie Cartan, S. P. Finikov
Creators: S. S. Chern, Vladislav V. Goldberg
Publisher: World Scientific Publishing Company
Category: Book
List Price: $58.00
Buy New: $57.24
You Save: $0.76 (1%)
New (11) Used (4) from $57.24
Rating:  1 reviews
Sales Rank: 1268003
Media: Hardcover
Pages: 300
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 9.3 x 6.1 x 0.8
ISBN: 981024746X
Dewey Decimal Number: 516.373
EAN: 9789810247461
Publication Date: May 2002
Availability: Usually ships in 1-2 business days
Shipping: International shipping available
Condition: Brand new. In stock. Exceptional customer service guaranteed!!!
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Product Description
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 1925-26. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 1926-27 were different - he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition.
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| Customer Reviews:
once overview, twice not suitable yet January 15, 2007
T. D. Atran (Richmond, VA USA)
1 out of 4 found this review helpful
As with all great masterpieces of math, I am not a critic for a good critique assumes expertise. I am an expert self-study beginner in pure and applied mathematics. My comments is for people in that disposition.
If you get a first look at the inside, then you quickly learn that the notation is very hard to understand for an introductory textbook. In addition, it is very dense and concise. Not much of an explanation to help first time beginners. It isn't meant to be introductory! I am sure that it is a standard classic for experts.
Elie Cartan was a truly great differential geometer! That is the reason I have the book; it's from a master.
In terms of approachability of the book, it is not that aproachable. If you are studying differential geometry, then it maybe right for you. I can say that I wanted an introductory self-study book and was disappointed.
It remains on the bookself and even got lost among other books for later review. When I have some more differential geometry courses or time I will try to decipher the notation. I can read math at the undergraduate level. This book is for sure for graduate students!
I just hope that in the future I can still make use of the book. I plan to go study differential geometry as a course with a professor. Then it would be nice to have something like this for reference work.
All in all, a masterpiece not easy to understand. It is how works of genius is. I better stick to reading math history books for introductions to math and self-studies. A better elementary book on Vector and Tensor Analysis is by Harry Lass which covers the fundamentals for elementary beginners like me. If you like Harry Lass's book then look forward to my other reviews. I am a struggling beginner that is not yet in graduate school for pure mathematics. Preparation is key and this book is an indication of what is ahead.
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