On Quasi-Generalized ϕ-recurrent Para-Kenmotsu Manifolds
Abstract
The object of this paper is to study and reveal the various geometric properties of quasi-generalized $\phi-$recurrent (briefly, $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$) para-Kenmotsu manifold. Among the results established here it is shown that a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an Einstein manifold. Moreover, we prove that a Ricci soliton in a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an expanding. Further, we study quasi-generalized $\mathcal{T}-\phi-$recurrent para-Kenmotsu manifold and obtain the results which reveal the nature of its associated 1-forms.
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