Geometry of generalized Ricci-type solitons on a class of Riemannian manifolds

In this paper, the notion of generalized Ricci-type soliton is introduced and its geometrical relevance on Riemannian CR-manifold is established. Particularly, it is shown that a Riemannian CR-manifold is Einstein when its metric is a generalized Ricci-type soliton. Next, it has been proved that a Riemannian CR-manifold is Einstein-like, when its metric is a generalized gradient Ricci-type almost soliton (or generalized Ricci-type almost soliton for which the soliton vector field is collinear to the CR-vector field). Finally, we present an example of generalized Ricci-type solitons which illustrate our results.(c) 2022 Elsevier B.V. All rights reserved.