The Geometry of δ-Ricci-Yamabe Almost Solitons on Para contact Metric Manifolds
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In this article we study a δ-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study δ-Ricci-Yamabe almost soliton and gradient δ-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a δ-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to ξ, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gra dient δ-Ricci-Yamabe almost soliton. We demonstrate a δ-Ricci-Yamabe almost soliton on a (κ, µ)-paracontact manifold.
Abstract
In this article we study a δ-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study δ-Ricci-Yamabe almost soliton and gradient δ-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a δ-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to ξ, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gra dient δ-Ricci-Yamabe almost soliton. We demonstrate a δ-Ricci-Yamabe almost soliton on a (κ, µ)-paracontact manifold.
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