黎曼流形中的近Yamabe孤立子  

Almost Yamabe Solitons in Riemannian Manifolds

作　　者：吴玉婷 刘建成 WU Yu-ting;LIU Jian-cheng(School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《西南师范大学学报（自然科学版）》2021年第4期25-28,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11761061).

摘　　要：主要研究了黎曼流形中的等距浸入近Yamabe孤立子.使用Hopf极大值原理及子流形的基本方程,得到了近Yamabe孤立子是全测地或全脐的充分条件.对欧氏单位球面Sn+1中的非平凡紧致极小梯度近Yamabe孤立子(Mn,g,f,ρ),证明了若Mn的数量曲率S≥n(n-2),则Mn等距于欧氏球面.In this paper,we study isometrical immersion of almost Yamabe solitons in a Riemannian manifold.By using Hopf's maximum principles and the basic equations of the submanifold,we obtain the sufficient conditions for submanifold to be totally geodesic,or totally umbilical.For a compact minimal gradient almost Yamabe solitons(Mn,g,f,ρ)in Euclidean sphere Sn+1,we prove that Mn isometrics to Euclidean sphere if its scalar curvature S≥n(n-2).

关 键 词：近Yamabe孤立子 极小浸入 全测地 全脐 

分 类 号：O186.12[理学—数学]