This book is an introduction to Cartan's approach to differential geometry.Two central methods in Cartan's geometry are the theory of exteriordifferential systems and the method of moving frames. This book presentsthorough and modern treatments of both subjects, including their applicationsto both classic and contemporary problems.It begins with the classical geometry of surfaces and basic Riemanniangeometry in the language of moving frames, along with an elementaryintroduction to exterior differential systems. Key concepts are developedincrementally with motivating examples leading to definitions, theorems, andproofs.Once the basics of the methods are established, the authors developapplications and advanced topics. One notable application is to complexalgebraic geometry, where they expand and update important results fromprojective differential geometry.The book features an introduction to $G$-structures and a treatment of thetheory of connections. The Cartan machinery is also applied to obtain explicitsolutions of PDEs via Darboux's method, the method of characteristics, andCartan's method of equivalence.
Search
Reviews
[Write a review of this article]
Find related articles from these CiteULike users
