A Rigidity Theorem for Affine Kähler-Ricci Flat Graph

Details A Rigidity Theorem for Affine Kähler-Ricci Flat Graph A Rigidity Theorem for Affine Kähler-Ricci Flat Graph

2007-10-19

arxiv.org/abs/0710.3637v2

Mathematics

Differential Geometry

24 pages

Scientific paper

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 J\"{o}rgens-Calabi-Pogorelov.

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