K-cosymplectic metric as an η-Ricci soliton

Abstract

Let M be an almost cosymplectic manifold such that the Reeb vector field is Killing. In this paper, it is proved that if the metric of M satisfying the [Formula: see text]-Einstein condition is an [Formula: see text]-Ricci soliton, then either M is Ricci flat or the potential vector field is an infinitesimal contact transformation. Also, a concrete example of cosymplectic [Formula: see text]-manifold admitting non-trivial Ricci and [Formula: see text]-Ricci solitons is constructed.