A study of ∗-Ricci–Yamabe solitons on LP-Kenmotsu manifolds

Abstract

In this study, we characterize $ LP $-Kenmotsu manifolds admitting $ * $-Ricci–Yamabe solitons ($ * $-RYSs) and gradient $ * $-Ricci–Yamabe solitons (gradient $ * $-RYSs). It is shown that an $ LP $-Kenmotsu manifold of dimension $ n $ admitting a $ * $-Ricci–Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by $ LP $-Kenmotsu manifolds. Finally, by using a non-trivial example of an $ LP $-Kenmotsu manifold, we verify some results of our paper.

Keywords

• $ * $-ricci–yamabe solitons
• $ lp $-kenmotsu manifolds
• einstein manifolds
• $ \eta $-einstein manifolds
• poisson's equation