CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM  

作　　者：徐辉阳 李策策 Huiyang XU;Cece LI(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,China)

机构地区：[1]School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023,China

出　　处：《Acta Mathematica Scientia》2023年第6期2413-2429,共17页数学物理学报（B辑英文版）

基　　金：supported by the NNSF of China (12101194,11401173).

摘　　要：In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

关 键 词：affine hypersurface semi-parallel cubic form Levi-Civita connection conformally flat warped product 

分 类 号：O186.11[理学—数学]