## Ricci solitons in almost $$f$$-cosymplectic manifolds.(English)Zbl 1395.53085

Summary: 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 dimensional almost $$f$$-cosymplectic is a cosymplectic manifold. Finally we classify a three dimensional $$\eta$$-Einstein almost $$f$$-cosymplectic manifold admitting a Ricci soliton.

### MSC:

 53D05 Symplectic manifolds (general theory) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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