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

In this paper, we characterize the η -Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an η -Einstein cosymplectic manifold M 2 n + 1 of dimension 2 n + 1 with n > 1 admits a gradient Einstein soliton, then either M 2 n + 1 is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of M 2 n + 1 . Also, we prove that if M 2 n + 1 admits a conformal vector field W , then either M 2 n + 1 is Ricci flat or W is homothetic. We also establish that a conformal vector field W on M 2 n + 1 is a strict infinitesimal contact transformation, provided the scalar curvature of M 2 n + 1 is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given. [ABSTRACT FROM AUTHOR]