Ricci solitons and gradient Ricci solitons in three-dimensional trans-Sasakian manifolds

By M. Turan, C. De, Ahmet Yildiz. 2012

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The object of the present paper is to study 3-dimensional trans-Sasakian manifolds admitting Ricci solitons and gradient Ricci solitons. We prove that if (1,V, λ) is a Ricci soliton where V is collinear with the characteristic vector field ξ, then V is a constant multiple of ξ and the manifold is of constant scalar curvature provided α, β =constant. Next we prove that in a 3-dimensional trans-Sasakian manifold with constant scalar curvature if 1 is a gradient Ricci soliton, then the manifold is either a β-Kenmotsu manifold or an Einstein manifold. As a consequence of this result we obtain several corollaries.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/716774ca4b541e3c8c62f9ab5ced6cce4badeaf4