Remarks on Einstein solitons with certain types of potential vector field

Abstract

We consider almost Einstein solitons $(V,\lambda )$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ 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.

References in corpus (1)

• Almost $\eta$-Ricci and almost $\eta$-Yamabe solitons with torse-forming potential vector field