Conformal vector field and gradient Einstein solitons on η-Einstein cosymplectic manifolds

Abstract

In this paper, we characterize the [Formula: see text]-Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an [Formula: see text]-Einstein cosymplectic manifold [Formula: see text] of dimension [Formula: see text] with [Formula: see text] admits a gradient Einstein soliton, then either [Formula: see text] is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of [Formula: see text]. Also, we prove that if [Formula: see text] admits a conformal vector field [Formula: see text], then either [Formula: see text] is Ricci flat or [Formula: see text] is homothetic. We also establish that a conformal vector field [Formula: see text] on [Formula: see text] is a strict infinitesimal contact transformation, provided the scalar curvature of [Formula: see text] is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given.