Abstract

In the present paper, we first investigate a Sasakian 3-metric as a quasi-Yamabe gradient soliton. In the sequel, extending the notions of quasi-Yamabe soliton and Ricci-Yamabe soliton, the notion of generalized Ricci-Yamabe soliton is introduced. It is shown that if (g, V, λ, α, β, γ) is a generalized gradient Ricci-Yamabe soliton on a complete Sasakian 3-manifold M with potential function f , then M is compact Einstein and locally isometric to a unit sphere. Moreover, the potential vector field V is an infinitesimal contact transformation and pointwise collinear with the characteristic vector field ξ. Further, if h is the Hodge-de Rham potential for V, then, upto a constant, f = h.

摘要

在本文中，我们首先研究了Sasakian 3-metric作为准Yabebe梯度孤子。在续集中，扩展了准Yamabe孤子和Ricci-Yamabe孤子的概念，引入了广义Ricci-Yamabe孤子的概念。结果表明，如果（g，V，λ，α，β，γ）是具有势函数f的完整Sasakian 3流形M上的广义梯度Ricci-Yamabe孤子，则M是紧的爱因斯坦且局部等距领域。此外，势矢量场V是无穷小的接触变换，并且与特征矢量场ξ呈点共线。此外，如果h是的Hodge-de Rham势V，直到一个常数，f = h。