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

Ivey, Thomas A.; Landsberg, J. M.

ISBN 10: 0821833758 / ISBN 13: 9780821833759

Published by Amer Mathematical Society, 2003

About this Item

Seller Inventory # BSM.10BU1

Bibliographic Details

• Title: Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
• Publisher: Amer Mathematical Society
• Publication Date: 2003
• Language: English
• ISBN 10: 0821833758
• ISBN 13: 9780821833759
• Binding: Hardcover
• Condition: very_good

About this title

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.

About the Author

Thomas A. Ivey: College of Charleston, Charleston, SC, Joseph M. Landsberg: Texas A&M University, College Station, TX