关于近拟常曲率空间中2-调和子流形  

On the 2-Harmonic Submaniflods of Nearly Quasi Constant Curvature Space

作　　者：叶闻 宋卫东 耿杰 YE Wen;SONG Weidong;Geng Jie(Anhui Institute of Information Technology,Wuhu 241000,China;School of Mathematics and Statistics,Anhui Normal University,Wuhu 241000,China)

机构地区：[1]安徽信息工程学院,安徽芜湖241000 [2]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2022年第1期13-17,共5页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11071005);高校优秀青年人才支持计划项目(gxyq2021254).

摘　　要：(N^(n+p),g)是n+p维单连通完备的黎曼流形,其黎曼曲率张量取如下形式K_(ABCD)=a(g_(AC)g_(BD)-g_(AD)g_(BC))+b(g_(AC)f_(BD)+g_(BD)f_(AC)-g_(AD)f_(BC)-g_(BC)f_(AD)),∑g^(AC)g^(BD)f_(AB)f_(CD)=1称n+p为近拟常曲率空间,本文利用活动标架法,研究此空间中的紧致2-调和子流形,得到了这类子流形关于其第二基本形式模长的Pinching定理及推广的J.Simons型积分不等式。Let N be a compact and connected Riemannian manifold,the Riemannian curvature tensor is in the following form:K_(ABCD)=a(g_(AC)g_(BD)-g_(AD)g_(BC))+b(g_(AC)f_(BD)+g_(BD)f_(AC)-g_(AD)f_(BC)-g_(BC)f_(AD)),∑g^(AC)g^(BD)f_(AB)f_(CD)=1,then we say N^(n+p)nearly quasi-constant curvature space.In this paper,the author studies the compact 2-harmonic submaniflods of a quast constant curvature space and obtains a pinching theorem of the length of the second fundamental form and an integral inequality of J.Simons-type.

关 键 词：近拟常曲率空间 2-调和子流形 极小子流形 J.Simons积分公式 

分 类 号：O186.16[理学—数学]