Characterizations of $\eta$-Ricci-Yamabe Solitons in Paracontact Geometry

Abstract

The purpose of this paper is to characterise $\eta$-Ricci-Yamabe solitons in paracontact geometry. Specifically, we investigate para-Kenmotsu manifolds admitting $\eta$-Ricci-Yamabe solitons and three-dimensional para-Kenmotsu manifolds satisfying gradient $\eta$-Ricci-Yamabe solitons. We also study para-Sasakian manifolds and para-cosymplectic manifolds obeying $\eta$-Ricci-Yamabe solitons and gradient $\eta$-Ricci-Yamabe solitons, respectively. As a consequence we obtain several interesting corollaries. Finally, we provide an example of $\eta$-Ricci-Yamabe solitons in a para-Kenmotsu manifold.

Keywords

• η-Ricci-Yamabe soliton (η-RYS)
• Paracontact geometry
• para-Kenmotsu (PK) manifolds; para-Sasakian (PS) manifolds; para-cosymplectic(PC) manifolds

Project Number

Not Applicable

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