黎曼流形中的近Yamabe孤立子

Almost Yamabe Solitons in Riemannian Manifolds

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).