η-Ricci--Yamabe and *-η-Ricci--Yamabe solitons in Lorentzian para-Kenmotsu manifolds

Abstract

Abstract The main purpose of this paper is to study η-Ricci–Yamabe solitons (η-RYS) and * {*} -η-Ricci–Yamabe solitons ( * {*} -η-RYS) in Lorentzian para-Kenmotsu n-manifolds (briefly, ( LPK ) n {(\mathrm{LPK})_{n}} ). We study the curvature condition R . S = 0 {R.S=0} and the cyclic parallel Ricci tensor in ( LPK ) n {(\mathrm{LPK})_{n}} admitting η-RYS. Furthermore, we study M-projectively flat and quasi-M-projectively flat Lorentzian para-Kenmotsu manifolds admitting * {*} -η-RYS. Finally, we give two examples of Lorentzian para-Kenmotsu manifolds admitting η-RYS and * {*} -η-RYS to verify some of our results.