紧致黎曼流形中的梯度Ricci-Yamabe孤立子  

Gradient Ricci-YamabeSoliton on a CompactRiemannian Manifold

作　　者：马彦芳 

机构地区：[1]西北师范大学,数学与统计学院,甘肃 兰州

出　　处：《理论数学》2023年第8期2388-2395,共8页Pure Mathematics

摘　　要：本文介绍了紧致黎曼流形M中具有势函数f的梯度Ricci-Yamabe孤立子(Mn,g,V,λ,α,β)的相关结果,其中,g为黎曼流形M上的黎曼度量,V是黎曼流形上的向量场,λ∈R为黎曼流形M的孤立子常数,α,β为常数。 首先得出紧致黎曼流形中具有共形向量场∇f的梯度Ricci-Yamabe孤立子的等距问题和平凡性结果,其次证明了梯度Ricci-Yamabe孤立子是稳定的或收缩的孤立子的条件,最后讨论不同分类下数量曲率的情况。This work aims to provide some results of gradient Ricci-Yamabe soliton with potentialf on a compact Riemmian manifold. g is Riemmian metric, V is vector field and α,β,λis constant on M. Firstly, the isometric notes and triviality results of Ricci-Yamabesoliton with conformal vector field on the compact Riemmian manifold are obtained.Then, I got the conditions that gradient Ricci-Yamabe soliton is steady or shrinking.Finally, scalar curvature under different classifications is discussed.

关 键 词：紧致黎曼流形 梯度Ricci-Yamabe孤立子 等距 数量曲率 共形向量场 

分 类 号：O18[理学—数学]