Geometry of Indefinite Kenmotsu Manifolds as *η-Ricci-Yamabe Solitons

Abstract

In this paper, we study the properties of (Formula presented.) -Kenmotsu manifolds if its metrics are (Formula presented.) -Ricci-Yamabe solitons. It is proven that an (Formula presented.) -Kenmotsu manifold endowed with a (Formula presented.) -Ricci-Yamabe soliton is (Formula presented.) -Einstein. The necessary conditions for an (Formula presented.) -Kenmotsu manifold, whose metric is a (Formula presented.) -Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence (Formula presented.) -Ricci-Yamabe solitons.