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

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 321-337.

• 论文 • 下一篇

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

许瑞伟*(),雷淼鑫()

河南师范大学数学与信息科学学院河南新乡 453007

收稿日期:2021-05-07 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 许瑞伟 E-mail:rwxu@htu.edu.cn;leimiaoxin0518@126.com
作者简介:雷淼鑫, E-mail: leimiaoxin0518@126.com
基金资助:
国家自然科学基金(11871197)

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

Ruiwei Xu*(),Miaoxin Lei()

School of Mathematics and Information Sciences, Henan Normal University, Henan Xinxiang 453007

Received:2021-05-07 Online:2022-04-26 Published:2022-04-18
Contact: Ruiwei Xu E-mail:rwxu@htu.edu.cn;leimiaoxin0518@126.com
Supported by:
the NSFC(11871197)

摘要/Abstract

摘要：

Fubini-Pick形式关于Blaschke-Berwald度量(或中心仿射度量)平行的局部强凸等仿射(或中心仿射)超曲面分类问题, 在过去十年内已被完全解决. 文献[20]对Fubini-Pick形式关于Calabi度量平行的2, 3维Calabi超曲面进行了分类, 该文将其推广到4维的情形.

关键词: 平行Fubini-Pick形式, Calabi几何, Graph浸入, Tchebychev仿射Kähler超曲面, 仿射极值超曲面

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

中图分类号:

O186.1

许瑞伟,雷淼鑫. ${\mathbb R}^5$中具有平行Fubini-Pick形式的Calabi超曲面的分类[J]. 数学物理学报, 2022, 42(2): 321-337.

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.

参考文献 20

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

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

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