紧致黎曼流形中的梯度Ricci-Yamabe孤立子

Gradient Ricci-YamabeSoliton on a CompactRiemannian Manifold

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。

Abstract: This work aims to provide some results of gradient Ricci-Yamabe soliton with potential f on a compact Riemmian manifold. g is Riemmian metric, V is vector field and α,β,λ is constant on M. Firstly, the isometric notes and triviality results of Ricci-Yamabe soliton 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.