Complete Hypersurfaces with Constant Laguerre Scalar Curvature in R^n  

作　　者：Jian Bo FANG Feng Jiang LI 

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

出　　处：《Acta Mathematica Sinica,English Series》2016年第6期715-724,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);supported by Scienticfic Research Fund of Yunnan Provincial Education Department(Grant No.2015Y101);Yunnan Applied Basic Research Young Project

摘　　要：Let x ： M^n-1→ R^n be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of M under the Laguerre transformation group of Rn are Laguerre form C and Laguerre tensor L. In this paper, we prove the following theorem： Let M be an （n-1）-dimensional （n 〉 3） complete hypersurface with vanishing Laguerre form and with constant Laguerre scalar curvature R in R^n, denote the trace-free Laguerre tensor by L = L -1/n-1tr（L）· Id. If supM ｜｜L｜｜=0,then M is Laguerre equivalent to a Laguerre isotropic hypersurface; and if supM ｜｜L^-｜｜≡√（n-1）（n-2）R/ （n-1）（n-2）（n-3） , M isLaguerre equivalent to the hypersurface x^- ： H^1× S^n-2 → R^n.Let x ： M^n-1→ R^n be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of M under the Laguerre transformation group of Rn are Laguerre form C and Laguerre tensor L. In this paper, we prove the following theorem： Let M be an （n-1）-dimensional （n 〉 3） complete hypersurface with vanishing Laguerre form and with constant Laguerre scalar curvature R in R^n, denote the trace-free Laguerre tensor by L = L -1/n-1tr（L）· Id. If supM ｜｜L｜｜=0,then M is Laguerre equivalent to a Laguerre isotropic hypersurface; and if supM ｜｜L^-｜｜≡√（n-1）（n-2）R/ （n-1）（n-2）（n-3） , M isLaguerre equivalent to the hypersurface x^- ： H^1× S^n-2 → R^n.

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]