LP-Kenmotsu Manifolds Admitting Bach Almost Solitons

Abstract

For a Lorentzian para-Kenmotsu manifold of dimension $m$ (briefly, ${(LPK)_{m}}$) admitting Bach almost soliton $(g,\zeta,\lambda)$, we explored the characteristics of the norm of Ricci operator. Besides, we gave the necessary condition for ${(LPK)_{m}}$ ($m\geq 4$) admitting Bach almost soliton to be an $\eta$-Einstein manifold. Afterwards, we proved that Bach almost solitons are always steady when a Lorentzian para-Kenmotsu manifold of dimension three has Bach almost soliton.

Keywords

• bach almost solitons
• $lp$-kenmotsu manifolds
• perfect fluid
• weyl tensor