Eta-Ricci Solitons on Lorentzian Para-Kenmotsu Manifolds

Abstract

The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $R\cdot S=0$. Further, we obtain results for $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $\eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $\eta$-quasi-conformally semi-symmetric, $\eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $\eta$-Ricci solitons.

Conformal η-Ricci soliton in Lorentzian para Kenmotsu manifolds

“…r(g) = −1 where r is the scalar curvature of the manifold, p is a scalar non dynamical field (time-dependent scalar field), p is also known as conformal pressure. For the study of curvature conditions on Lorentzian para-Kenmotsu and Lorentzian para-Sasakian manifolds, we request to the reader please refer ( [1], [8], [12], [15], [17][18]).…”