${\mathbb R}^5$中具有平行Fubini-Pick形式的Calabi超曲面的分类

Abstract

Abstract:

The classifications of locally strongly convex equiaffine hypersurfaces (centroaffine hypersurfaces) with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Blaschke-Berwald metric (centroaffine metric) have been completed in the last decades. In [20], the authors studied Calabi hypersurfaces with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Calabi metric and classified 2 and 3-dimensional cases. In this paper, we extend such calssification results to 4-dimensional Calabi hypersurfaces in the affine space ${\mathbb R}^5$ .

Key words: Parallel Fubini-Pick form, Calabi geometry, Graph immersion, Tchebychev affine Kähler hypersurface, Affine extremal hypersurface

CLC Number:

O186.1

Ruiwei Xu,Miaoxin Lei. Classification of Calabi Hypersurfaces in ${\mathbb R}^5$ with Parallel Fubini-Pick Form[J].Acta mathematica scientia,Series A, 2022, 42(2): 321-337.

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References

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Classification of Calabi Hypersurfaces in ${\mathbb R}^5$ with Parallel Fubini-Pick Form

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Classification of Calabi Hypersurfaces in R5{\mathbb R}^5 with Parallel Fubini-Pick Form

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Classification of Calabi Hypersurfaces in ${\mathbb R}^5$ with Parallel Fubini-Pick Form