Geometry of δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds

Abstract

In this article, we studied δ-almost Yamabe solitons within the framework of paracontact metric manifolds. First, we proved that for a paracontact metric manifold M , if a paracontact metric g represents a δ-almost Yamabe soliton associated with the potential vector field Z being an infinitesimal contact transformation, then Z is Killing, and if the potential vector field Z is collinear with ξ, then the manifold M is K -paracontact. Next, if we take a K -paracontact metric manifold admitting δ-almost Yamabe soliton with the potential vector field Z parallel to the characteristic vector field and with constant scalar curvature then either the scalar curvature will vanish or g becomes a δ-Yamabe soliton under a certain condition. We established some results on K -paracontact manifolds admitting δ-almost gradient Yamabe solitons. Moreover, we consider a (k, µ)-paracontact metric manifold admitting a non-trivial δ-almost gradient Yamabe soliton. We have shown that the potential vector field Z is parallel to ξ. We have also discussed δ-almost gradient Yamabe solitons on the para-Sasakian manifold. Finally, we consider a para-cosymplectic manifold with a δ-almost Yamabe soliton. In the end, we construct two examples of K -paracontact metric manifolds with δ-almost Yamabe soliton.