R^(5)中具有平行Fubini-Pick形式的Calabi超曲面的分类  

Classification of Calabi Hypersurfaces in R^(5) with Parallel Fubini-Pick Form

作　　者：许瑞伟[1] 雷淼鑫 Xu Ruiwei;Lei Miaoxin(School of Mathematics and Information Sciences,Henan Normal University,Henan Xinxiang 453007)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《数学物理学报（A辑）》2022年第2期321-337,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871197)。

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.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 R^(5).

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 

分 类 号：O186.1[理学—数学]