On 3-Dimensional Trans-Sasakian Manifolds Admitting ⁎−Ricci Solitons

Abstract

The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds admitting ∗-Ricci solitons. First, 3-dimensional trans-Sasakianmanifolds admitting ∗-Ricci solitons satisfying the conditions R(ξ, .) · S, S(ξ, .) ·
R = 0 and Q · R = 0 are studied. Further, 3-dimensional manifolds admitting ∗-Ricci solitons satisfying certain conditions on the projective curvature tensor are considered and obtained several interesting results. Finally, the existence of ∗-Ricci solitons in a 3-dimensional trans-Sasakian manifold has been proved by a concrete example.

Key words and phrases. ∗-Ricci solitons, trans-Sasakian manifolds, projective curvature tensor, Einstein manifold.

2000 Mathematics Subject Classification. 53C15, 53C25