Remarks on Einstein solitons with certain types of vector field

Abstract

We consider almost Einstein solitons ( V, λ ) in a Riemannian manifold when V is a gradient, a solenoidal or a concircular vector field. We explicitly express the function λ by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.