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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics) - Hardcover
Synopsis
This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems.
It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs.
Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry.
The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence.
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About the Author
Thomas A. Ivey: College of Charleston, Charleston, SC, Joseph M. Landsberg: Texas A&M University, College Station, TX
Review
[T]his book, like the first edition, is an excellent source for graduate students and professional mathematicians who want to learn about moving frames and G-structures in trying to understand differential geometry. --Thomas Garrity, Mathematical Reviews
All the material is carefully developed, many examples supporting the understanding. The reviewer warmly recommends this volume to mathematical university libraries. --Gabriel Eduard Vilcu, Zentralblatt MATH
"About this title" may belong to another edition of this title.
- PublisherAmer Mathematical Society
- Publication date2003
- ISBN 10 0821833758
- ISBN 13 9780821833759
- BindingHardcover
- LanguageEnglish
- Number of pages378
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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821833758
ISBN 13: 9780821833759
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Hardcover
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Condition: Good. Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. Seller Inventory # Z1-A-011-03105
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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821833758
ISBN 13: 9780821833759
Used
Hardcover
Seller: Book Alley, Pasadena, CA, U.S.A.
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Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems.
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Providence: American Mathematical Society, 2003
ISBN 10: 0821833758
ISBN 13: 9780821833759
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Hardback. Condition: Very Good. Series: Graduate Studies in Mathematics. xiv 378p hardback in very good condition, glossy blue and yellow laminated boards, tight binding, clean and bright pages, a bit of light foxing to endpapers, otherwise like new with no noticeable wear or markings Language: English Weight (g): 3000. Seller Inventory # 233511
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