On Laguerre Form and Laguerre Isoparametric Hypersurfaces  

作　　者：Jian Bo FANG 

机构地区：[1]Department of Mathematics, Tongji University [2]School of Mathematics and Statistics, Chuxiong Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第3期501-510,共10页数学学报（英文版）

基　　金：Supported by Scienticfic Research Fund of Yunnan Provincial Education Department(Grant No.2014Y445)

摘　　要：Let x ： M^n-1→ R^nbe an umbilical free hypersurface with non-zero principal curvatures.M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and has constant Lauerre principal curvatures. In this paper, under the condition of having constant Laguerre principal curvatures, we show that the hypersurface is of vanishing Laguerre form if and only if its Laguerre form is parallel with respect to the Levi-Civita connection of its Laguerre metric.Let x ： M^n-1→ R^nbe an umbilical free hypersurface with non-zero principal curvatures.M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and has constant Lauerre principal curvatures. In this paper, under the condition of having constant Laguerre principal curvatures, we show that the hypersurface is of vanishing Laguerre form if and only if its Laguerre form is parallel with respect to the Levi-Civita connection of its Laguerre metric.

关 键 词：Laguerre isoparametric hypersurface Laguerre second fundamental form Laguerre metric Laguerre form parallel Laguerre form 

分 类 号：O186.11[理学—数学] O171[理学—基础数学]