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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.
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