$\bbr^{n+1}$中具有平行Fubini-Pick型的Calabi超曲面分类
微分几何
2021-12-06 v1
摘要
具有相对于Blaschke-Berwald仿射度量（相应地为中仿射度量）的Levi-Civita联络的平行Fubini-Pick型的局部强凸等仿射超曲面（相应地为中仿射超曲面）的分类已在过去几十年由几位几何学家完成，见\cite{HLV}和\cite{CHM}。本文在Calabi几何中定义广义Calabi积，并依据其Calabi不变量证明分解定理。作为主要结果，我们得到了中具有相对于Calabi度量的Levi-Civita联络的平行Fubini-Pick型的Calabi超曲面的完整分类。该结果是等仿射情形\cite{HLV}与中仿射情形\cite{CHM}分类定理在Calabi几何中的对应物。
引用
@article{arxiv.2112.01947,
title = {Classification of Calabi Hypersurfaces in $\bbr^{n+1}$ with parallel Fubini-Pick form},
author = {Miaoxin Lei and Ruiwei Xu},
journal= {arXiv preprint arXiv:2112.01947},
year = {2021}
}
备注
For covinent readers' convenience, we keep many detailed calculations and proofs of conclusions. Most of them are the same in [10] and [6]. Comments are welcome