ENGLISH

Cartan for beginners: differential geometry via moving frames

By Thomas A. Ivey , J. M. Landsberg

Book information

Publisher
American Mathematical Society,
Year
2003
ISBN
9780821833759, 0821833758
Open Library ID
OL16000847M
Language
english
Format
DJVU
Filesize
3 MB (2634687 bytes)
Series
Graduate Studies in Mathematics
Pages
392\392
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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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