Laguerre Isopararmetric Hypersurfaces in R^4  

作　　者：Tong Zhu LI Hua Fei SUN 

机构地区：[1]Department of Mathematics,Beijing Institute of Technology

出　　处：《Acta Mathematica Sinica,English Series》2012年第6期1179-1186,共8页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10801006);supported by National Natural Science Foundation of China (Grant No. 10871218)

摘　　要：Let x ： M →R^n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in R^4.Let x ： M →R^n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in R^4.

关 键 词：Laguerre transformation group Laguerre isoparametric hypersurface Laguerre second fundamental form 

分 类 号：O186.11[理学—数学]