Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold

Abstract

In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type (α,β) admits a Ricci soliton where the covariant derivative of potential vector field V in the direction of unit vector field ξ is orthogonal to ξ. It is also demonstrated that if the structure functions meet α2=β2, then the covariant derivative of V in the direction of ξ is a constant multiple of ξ. Furthermore, the nature of scalar curvature is evolved when the manifold of type (α,β) satisfies *-conformal Ricci soliton, provided α≠0. Finally, an example is presented to verify the findings.