Cartan For Beginners: Differential Geometry Via Moving Frames And Exterior Differential Systems (graduate Studies In Mathematics)
by Thomas A. Ivey /
2003 / English / DjVu
7.6 MB Download
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.
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.
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.
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.
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.
