- Hardcover: 300 pages
- Publisher: World Scientific Publishing (Dec 10 2001)
- Language: English
- ISBN-10: 981024746X
- ISBN-13: 978-9810247461
- Product Dimensions: 23.7 x 15.5 x 2 cm
- Shipping Weight: 562 g
- Amazon Bestsellers Rank: #2,156,223 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Details |
Product Description
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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1. Components of an infinitesimal displacement. Consider an ordinary three-dimensional Euclidean space. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
1. Components of an infinitesimal displacement. Consider an ordinary three-dimensional Euclidean space. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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2 reviews
Power of Thought
Nov 19 2011
Before you read this book, please note that you have a sound foundation of differential geometry on surface ( Do Carmo has a very good text book on it ).
I have heard a lot of complaints like - they don't understand Master's work of their time or just simply said it is over-simplied - This book is a truly master work: it is the direct extension of the geometry on surface - an orthogonal frame is used and imply more - how to generate results to Cantan's moving frame.
A good book not only teach knowledges to student, but reveal the intellectual pathway to the problem. From this criteria, I give the highest mark to this book.
I have heard a lot of complaints like - they don't understand Master's work of their time or just simply said it is over-simplied - This book is a truly master work: it is the direct extension of the geometry on surface - an orthogonal frame is used and imply more - how to generate results to Cantan's moving frame.
A good book not only teach knowledges to student, but reveal the intellectual pathway to the problem. From this criteria, I give the highest mark to this book.
2 of 8 people found the following review helpful
once overview, twice not suitable yet
Jan 15 2007
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.
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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