Certain results on Ricci solitons in α-Kenmotsu manifolds

R. Kumar , A. Mourya

Science Vision 18 (1), 11-15 | Published on 31 March 2018 | https://doi.org/10.33493/scivis.18.01.02

Abstract

In this paper, we study some curvature problems of Ricci solitons in α-Kenmotsu manifold. It is shown that a symmetric parallel second order-covariant tensor in a α-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (Lvg + 2S) is parallel where V is a given vector field, then the structure (g, V, λ) yield a Ricci soliton. Further, by virtue of this result, Ricci solitons for n-dimentional α-Kenmotsu manifolds are obtained. In the last section, we discuss Ricci soliton for 3-dimentional α-Kenmotsu manifolds.

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