Three-dimensional trans-Sasakian manifolds and solitons

Purpose The authors set the goal to find solution of Eisenhart problem within framework three-dimensional trans-Sasakian manifolds. Also, they prove some results Ricci solitons, η -Ricci solitons and weakly  symmetric Finally, give a nontrivial example proper manifold. Design/methodology/approach have used tensorial approach achieve goal. Findings A second-order parallel tensor on manifold is constant multiple associated Riemannian metric g . Originality/value declare that manuscript original it has not been submitted any other journal for possible publication.