摘要
设M是双曲空间中具有平行平均曲率的完备子流形,Φ是M的无迹第二基本形式.本文证明了在子流形任意测地球上|Φ|的L^2模小于二次增长条件下,sup_x∈M|Φ|~2(x)小于某常数或者|Φ|的L^n模小于某常数时,M是全脐的,这一结果推广了完备极小子流形的相关结果.
Let M be a complete submanifold with parallel mean curvature in a hyperbolic space andΦbe the traceless second fundamental form of M.In this paper,it is shown that the submanifold is totally umbilical if the L^2 norm of|Φ|has less than quadratic growth on any geodesic ball of M and either supn_x∈M|Φ|~2(x)is less than some constant or L^n norm of|Φ|is less than some constant.This is a generalization of the results on complete minimal submanifolds.
作者
周俊东
ZHOU Jundong(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;School of Mathematics and Statistics,Fuyang Normal University,Fuyang Anhui 236037,China)
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2020年第2期8-14,共7页
Journal of East China Normal University(Natural Science)
基金
安徽省自然科学研究重点项目(KJ2017A341)
阜阳师范学院青年人才基金(RCXM201714)
阜阳师范学院教学工程项目(2017JYXM29).
关键词
双曲空间
无迹第二基本形式
第一特征值
hyperbolic space
traceless second fundamental form
the first eigenvalue
