Ricci solitons in almost $f$-cosymplectic manifolds

Abstract

In this article we study an almost $f$-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic $(\kappa ,\mu )$-manifold. Further, we consider an almost $f$-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector field and show that a three dimesional almost $f$-cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional $\eta$-Einstein almost $f$-cosymplectic manifold admitting a Ricci soliton.

We correct the Theorem 1.1 and its proof

References in corpus (2)

• A survey on cosymplectic geometry
• Sasakian metric as a Ricci soliton and related results