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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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