Geometry of paracontact metric as an almost Yamabe solitons

Abstract

In this offering exposition, we intend to study paracontact metric manifold [Formula: see text] admitting almost Yamabe solitons. First, for a general paracontact metric manifold, it is proved that [Formula: see text] is Killing if the vector field [Formula: see text] is an infinitesimal contact transformation and that [Formula: see text] is [Formula: see text]-paracontact if [Formula: see text] is collinear with Reeb vector field. Second, we proved that a [Formula: see text]-paracontact manifold admitting a Yamabe gradient soliton is of constant curvature [Formula: see text] when [Formula: see text] and for [Formula: see text], the soliton is trivial and the manifold has constant scalar curvature. Moreover, for a paraSasakian manifold admitting a Yamabe soliton, we show that it has constant scalar curvature and [Formula: see text] is Killing when [Formula: see text]. Finally, we consider a paracontact metric [Formula: see text]-manifold with a non-trivial almost Yamabe gradient soliton. In the end, we construct two examples of paracontact metric manifolds with an almost Yamabe soliton.