Indian Journal of Science and Technology

Abstract

Objectives: The present paper is to study certain types of metric such as 􀀀h-Ricci-Yamabe soliton on Lorentzian Para-Sasakian manifolds with respect to semi-symmetric non-metric connection. Methods: It includes Contraction, Lie derivative, Semi-symmetric non-metric connection, Gradient, Laplacian equation, 􀀀h-Ricci-Yamabe soliton. Findings: We get some curvature properties of Lorentzian Para-Sasakian manifolds admitting semi-symmetric non-metric connection. Here, we develop the relation of soliton constant on Lorentzian Para- Sasakian manifold admitting 􀀀h-Ricci-Yamabe soliton with respect to semi-symmetric non-metric connection. Later, we have acquired Laplacian equation from 􀀀h-Ricci-Yamabe soliton when the potential vector field x of the soliton is of gradient types. Finally, we have shown the nature of the solitons when the vector field is conformally killing admitting semisymmetric non-metric connection. Novelty: This work has not been done by any other authors.

Keywords: Ricci Yamabe solitons, 􀀀h-Ricci-Yamabe soliton, conformal killing vector field, 􀀀h-Einstien soliton, Lorentzian Para-Sasakian manifold Mathematics Subject Classification (2020). 53C15,53C25,53C43.