A Rigidity Theorem for Affine Kähler-Ricci Flat Graph

Abstract

It is shown that any smooth strictly convex global solution of $$\det (\frac{{\partial }^{2}u}{\partial {\xi }_i\partial {\xi }_j})=\exp \left\{-\sum _{i=1}^n{d}_i\frac{\partial u}{\partial {\xi }_i}-d_0\right\},$$ where $d_0$, $d_1$,...,$d_n$ are constants, must be a quadratic polynomial. This extends a well-known theorem of Jörgens-Calabi-Pogorelov.

24 pages