On Affine Hypersurfaces with Parallel Cubic Form Relative to Affineα-connection  

作　　者：Ce Ce LI Cheng XING Hui Yang XU 

机构地区：[1]School of Mathematics and Statistics,He’nan University of Science and Technology,Luoyang 471023,P.R.China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1099-1114,共16页数学学报（英文版）

基　　金：supported by NNSF of China(Grant No.11401173);supported by NNSF of China(Grant No.12171437);supported by NNSF of China(Grant No.12101194)。

摘　　要：Similar to Nomizu-Pinkall's geometric characterization of the Cayley surface and Hu-Li-Zhang's characterization of the Cayley hypersurface,how can one characterize the generalized Cayley hypersurfaces?In this paper,by the affineα-connection of statistical manifolds,we study affine hypersurfaces with parallel cubic form relative to the affineα-connection.As the main results,we complete the classification of such hypersurfaces if its affine metric is either definite,or Lorentzian withα≠-1.Moreover,we give a new characterization of the generalized Cayley hypersurfaces to answer the question.

关 键 词：Affine hypersurface parallel cubic form affineα-connection Einstein metric 

分 类 号：O186.11[理学—数学]