紧致黎曼流形中的梯度Ricci-Yamabe孤立子

Gradient Ricci-YamabeSoliton on a CompactRiemannian Manifold

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.