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arXiv · 0710.3637

A Rigidity Theorem for Affine Kähler-Ricci Flat Graph

An-Min Li·Ruiwei Xu
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Abstract

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

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An-Min Li, Ruiwei Xu. 2007-10-20. A Rigidity Theorem for Affine Kähler-Ricci Flat Graph. https://arxiv.org/abs/0710.3637

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