λ-超曲面的一个积分等式  

A Rigidity Theorem ofλ-Hypersurfaces

作　　者：李云川[1] 刘燕 魏国新[3] LI Yunchuan;LIU Yan;WEI Guoxin(Department of Business Tourism, Henan College of Transportation, Zhengzhou 451460, China;School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China;School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China)

机构地区：[1]河南交通职业技术学院商务旅游系,郑州451460 [2]郑州航空工业管理学院数学学院,郑州450046 [3]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2020年第4期104-106,共3页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11771154);广东省高等学校珠江学者岗位计划项目(2018);广东省自然科学基金项目(2019A1515011451)。

摘　　要：研究了λ-超曲面,得到了有关完备的λ-超曲面的一个积分等式:若X:M→R^n+1是n-维完备的具有多项式面积增长的λ-超曲面且满足S有界,则有∫M(|▽H|^2+(H-λ)(H+S(λ-H)))e-|X|^2/2 dμ=0,其中,H是M的平均曲率,S是M的第二基本形式模长平方.并由该积分等式得到了一个刚性结果.λ-hypersurfaces are studied and a rigidity result about completeλ-hypersurfaces is given.If X:M→R^n+1 is an n-dimensional completeλ-hypersurface with polynomial area growth and satisfies S bounded,then∫M(|▽H|^2+(H-λ)(H+S(λ-H)))e-|X|^2/2 dμ=0,where H is the mean curvature of M,S is the squared norm of the second fundamental form of M.As an application of the integral equation,a rigidity result about completeλ-hypersurfaces is obtained.

关 键 词：平均曲率 加权面积泛函 λ-超曲面 

分 类 号：O186.16[理学—数学]