SOME GEOMETRIC PROPERTIES OF PARA-KENMOTSU MANIFOLDS ADMITTING $Q \varphi=\varphi Q$

Hereby, some geometric properties such as $\varphi-$ Ricci symmetric, weakly $\varphi$-Ricci symmetric and Ricci-Yamabe soliton as well as parallel 2-form of the para-Kenmotsu manifolds admitting $Q \varphi=\varphi Q$ are discussed. This paper also deals with Ricci-Yamabe soliton on para-Kenmotsu manifold admitting the curvature condition $\mathbf{\widetilde{R}(\xi,\x_1).\s=0}$ and locally $\varphi-$ Ricci symmetric para-Kenmotsu manifolds of dimension three. Together with we have cited some examples of 3-dimensional $\varphi-$ Ricci symmetric and locally $\varphi-$ Ricci symmetric para-Kenmotsu manifold.