Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)

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9780821833759: Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
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Book by Ivey Thomas A Landsberg J M

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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. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.

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9781470409869: Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)

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ISBN 10:  1470409860 ISBN 13:  9781470409869
Editorial: American Mathematical Society, 2016
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Descripción American Mathematical Society, United States, 2003. Hardback. Condición: New. UK ed.. Language: English . Brand New Book. 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. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. Nº de ref. del artículo: AAZ9780821833759

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Descripción American Mathematical Society, United States, 2003. Hardback. Condición: New. UK ed.. Language: English . Brand New Book. 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. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. Nº de ref. del artículo: AAZ9780821833759

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Descripción American Mathematical Society, 2003. Condición: New. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents the treatments of both subjects, including their applications to both classic and contemporary problems. It features an introduction to $G$-structures and a treatment of the theory of connections. Series: Graduate Studies in Mathematics. Num Pages: 378 pages, Illustrations. BIC Classification: PBKJ; PBMP; PBMW; PBPD; PBW. Category: (P) Professional & Vocational. Dimension: 186 x 262 x 25. Weight in Grams: 826. . 2003. Hardcover. . . . . . Nº de ref. del artículo: V9780821833759

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