Ricci-Yamabe solitons and 3-dimensional Riemannian manifolds

Abstract

In this paper, we classify 3-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are Ricci-Yamabe solitons and gradient Ricci-Yamabe solitons, respectively. Finally, we construct an example to illustrate our result.