?-Conformally Flat LP-Kenmotsu Manifolds and Ricci-Yamabe Solitons

In the present paper, we characterize m-dimensional zeta-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 delta r=4(m-1)/delta{beta(m-1)+rho}+2(m-3)r - 4m(m-1)(m-2), where rho,delta(&NOTEQUexpressionL; 0) is an element of 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.