<i>ζ</i>-Conformally Flat <i>LP</i>-Kenmotsu Manifolds and Ricci–Yamabe Solitons

Abstract

In the present paper, we characterize m-dimensional ζ-conformally flat LP-Kenmotsu manifolds (briefly, (LPK)m) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (LPK)m admitting an RYS satisfies the Poisson equation Δr=4(m−1)δ{β(m−1)+ρ}+2(m−3)r−4m(m−1)(m−2), where ρ,δ(≠0)∈R. In this sequel, the condition for which the scalar curvature of an (LPK)m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an (LPK)m. Finally, a non-trivial example of an LP-Kenmotsu manifold (LPK) of dimension four is constructed to verify some of our results.

Keywords

• Lorentzian manifolds
• Ricci–Yamabe solitons
• gradient Ricci–Yamabe solitons
• perfect fluid spacetime
• Einstein manifolds