Generalized Bach solitons on (κ,μ)′-almost-Kenmotsu manifolds and its applications in perfect fluid spacetimes

Abstract

The principal aim of this paper is to find the expression of *-Bach tensors on [Formula: see text]-almost-Kenmotsu manifolds. It is shown that if the metric of a [Formula: see text]-almost-Kenmotsu manifold admits a generalized closed *-Bach soliton, then the metric is *-Bach flat under certain restrictions. We also prove that the metric of a generalized gradient *-Bach soliton on a [Formula: see text]-almost-Kenmotsu manifold is *-Bach flat, for a soliton function which is invariant under the Reeb vector field. Further, we characterize generalized *-Bach solitons with trace-free *-Bach tensors on [Formula: see text]-almost-Kenmotsu manifolds and results are verified by an example. As an application of these solitons, we study generalized almost-Bach solitons whose metrics are associated with the Lorentzian metric of the perfect fluid spacetimes.