Geometry of {\delta}-almost gradient Yamabe solitons on pseudo-Riemannian manifolds

TL;DR

This paper investigates { extdelta}-almost Yamabe solitons on various types of para-contact metric manifolds, establishing conditions under which the potential vector field is Killing or parallel, and providing examples of such structures.

Contribution

It characterizes { extdelta}-almost Yamabe solitons on para-contact manifolds, revealing conditions for the potential vector field and scalar curvature, and constructs explicit examples.

Findings

Potential vector field Z is Killing when Z is an infinitesimal contact transformation.

If Z is collinear with , the manifold is K-paracontact.

On para-Sasakian manifolds, specific conditions for { extdelta}-almost gradient Yamabe solitons are established.

Abstract

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