Remarks on Gap Theorems for Complete Hypersurfaces with Constant Scalar Curvature  

作　　者：Jin-Chuan Bai Yong Luo 

机构地区：[1]Science Research Center,Chongqing University of Technology,Chongqing 400054,China

出　　处：《Journal of Mathematical Study》2023年第3期279-290,共12页数学研究（英文）

基　　金：supported by the NSF of China(Grant No.12271069);the Chongqing NSF(Grant No.cstc2021jcjy-msxmX0443).

摘　　要：Assume that Mn(n≥3)is a complete hypersurface in Rn+1 with zero scalar curvature.Assume that B,H,g is the second fundamental form,the mean curvature and the induced metric of M,respectively.We prove that M is a hyperplane if-P_(1)(■H,■|H|)≤-δ|H||■H|^(2)for some positive constantδ,where P1=nHg−B which denotes the first order Newton transformation,and(∫_(M|H|^(n)dv)1/n<afor some small enough positive constantαwhich depends only on n andδ.We also derive similar result for complete hypersurfaces in Sn+1 with constant scalar curvature R=n(n−1).

关 键 词：HYPERSURFACES constant scalar curvature gap theorem 

分 类 号：O17[理学—数学]