Global Affine Differential Geometry of Hypersurfaces

2. revised and extended Auflage 2015
ISBN: 978-3-11-026667-2
Verlag: De Gruyter

Buch, Englisch, Band 11, 367 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 819 g

Reihe: De Gruyter Expositions in Mathematics

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.

Zielgruppe

Graduate students in differential geometry and PDEs, researchers

Autoren/Hrsg.

Li, An-Min

Hu, Zejun

Simon, Udo

Zhao, Guosong

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Über Autor(innen)

Z. Hu, Zhenzhou Univ., China; A.-M. Li, Sichuan Univ./Chinese AoS, China; U. Simon, TU Berlin, Germany; G. Zhao, Sichuan Univ., China.