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Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 175) by Thomas A. Ivey, Joseph M. Landsberg is a nonfiction available to read on EtoBox.

What is Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 175) about?

Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) 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 in geometry. It begins with the classical differential 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. As well, the book features an introduction to $G$-structures and a treatment of the theory of connections. The techniques of EDS are 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 different

Who reads Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 175)?

Author

Thomas A. Ivey, Joseph M. Landsberg

Publisher

American Mathematical Society

Published

2016

Language

EN

ISBN

9781470435912

Category

nonfiction

Subjects

Mathematics, Geometry And Topology, Stem