Generalized solitonic characteristics in trans para Sasakian manifolds

Abstract

In the current research, we quantify the almost generalized Ricci soliton on the trans-para-Sasakian manifold as well as the gradient almost generalized Ricci soliton. Trans-para Sasakian manifolds that meet certain criteria are also required to be Einstein manifolds. It is demonstrated that the almost generalized Ricci soliton equation is also satisfied by some manifolds, notably $\alpha$-para-Sasakian and $\beta$-para -Kenmotsu manifolds. The fact that a compact trans-para-Sasakian admits both a convex Einstein potential with non-negative scalar curvature and a gradient almost generalized Ricci soliton with Hodge-de Rham potential has also been covered.