Soliton on Sasakian manifold endowed with quarter-symmetric non-metric connection on the tangent bundle

Purpose The purpose of this paper is to study the properties of the solitons on Sasakian manifold on the tangent bundle with respect to quarter symmetric non metric connection. Design/methodology/approach We used the vertical and complete lifts, Ricci solitons, tangent bundle, Einstein manifold, partial differential equation, Einstein semi-symmetric. Findings In the proposed paper, we study the complete lift of the Ricci soliton on Sasakian manifold endowed with quarter-symmetric non-metric connection (QSNMC) on the tangent bundle and discuss its curvature properties. The complete lift of the Ricci soliton on Sasakian manifold with QSNMC is investigated and it was found to be η-Einstein manifold on the tangent bundle. We study several properties of the complete lift of the Ricci soliton on Sasakian manifold with QSNMC satisfying certain conditions. Also the complete lifts of the Ricci soliton on Φ-recurrent and Einstein semi-symmetric Sasakian manifolds on the tangent bundle are studied and some theorems are also proved. Originality/value The present author carried out this research in extension of studying the properties of differentiable manifold using lifting theory.