2015/07/30 by An-Min Li, Udo Simon, Guosong Zhao +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Library science #Mathematics #Art history #Humanities #Art #Computer science
paper · doi:10.1515/9783110268898
openalex publication_date 2015/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.