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\(\eta\)-Ricci soliton on 3-dimensional \(f\)-Kenmotsu manifolds. (English) Zbl 1408.53065

Summary: The object of the present paper is to carry out \(\eta\)-Ricci soliton on 3-dimensional regular \(f\)-Kenmotsu manifold and we turn up some geometrical results. Furthermore we bring out the curvature conditions for which \(\eta\)-Ricci soliton on such manifolds are shrinking, steady or expanding. We wind up by considering examples of existence of shrinking and expanding \(\eta\)-Ricci soliton on 3-dimensional regular \(f\)-Kenmotsu manifolds.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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