Description
Book SynopsisTwo 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.
Trade Review[T]his book, like the first edition, is an excellent source for graduate students and professional mathematicians who want to learn about moving frames and G-structures in trying to understand differential geometry." - Thomas Garrity,
Mathematical Reviews"All the material is carefully developed, many examples supporting the understanding. The reviewer warmly recommends this volume to mathematical university libraries." - Gabriel Eduard Vilcu,
Zentralblatt MATHTable of Contents
- Moving frames and exterior differential systems
- Euclidean geometry
- Riemannian geometry
- Projective geometry I: Basic definitions and examples
- Cartan-Kahler I: Linear algebra and constant-coefficient homogeneous systems
- Cartan-Kahler II: The Cartan algorithm for linear Pfaffian systems
- Applications to PDE
- Cartan-Kahler III: The general case
- Geometric structures and connections
- Superposition for Darboux-integrable systems
- Conformal differential geometry
- Projective geometry II: Moving frames and subvarieties of projective space
- Linear algebra and representation theory
- Differential forms
- Complex structures and complex manifolds
- Initial value problems and the Cauchy-Kowalevski theorem
- Hints and answers to selected exercises
- Bibliography
- Index.
