?-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.

Automated summary

In this paper, we study m-dimensional zeta-conformally flat LP-Kenmotsu manifolds (abbreviated as (LPK)(m)) equipped with Ricci-Yamabe solitons (RYS) and gradient Ricci-Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (LPK)(m) with 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. Furthermore, the condition for the scalar curvature of an (LPK)(m) with an RYS to satisfy the Laplace equation is established. An affirmative answer is also given for the existence of a GRYS on an (LPK)(m). Finally, a non-trivial example of a four-dimensional LP-Kenmotsu manifold (LPK) is constructed to validate some of the results.