The aim of the present paper is to study 3-dimensional f-Kenmotsu manifolds and Ricci solitons. First, we give an example of a 3-dimensional f-Kenmotsu manifold. Then we consider a Riccisemisymmetric 3-dimensional f-Kenmotsu manifold and prove that a 3-dimensional f-Kenmotsu manifold is Ricci semisymmetric if and only if it is an Einstein manifold. Moreover, we investigate an η-parallel Ricci tensor in a 3-dimensional f-Kenmotsu manifold. Finally, we study Ricci solitons in a 3-dimensional f-Kenmotsu manifold.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 5, pp. 620–628, May, 2013.
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Yildiz, A., De, U.C. & Turan, M. On 3-dimensional f-Kenmotsu manifolds and Ricci solitons. Ukr Math J 65, 684–693 (2013). https://doi.org/10.1007/s11253-013-0806-6
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DOI: https://doi.org/10.1007/s11253-013-0806-6