This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry - as differential geometry in general - has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.
- ISBN10 3110390906
- ISBN13 9783110390902
- Publish Date 17 August 2015 (first published 1 January 1993)
- Publish Status Active
- Out of Print 9 April 2021
- Publish Country DE
- Imprint De Gruyter
- Edition 2nd revised and extended edition
- Format eBook
- Pages 376
- Language English
- URL https://degruyter.com/isbn/9783110390902