Geometry of paracontact metric as an almost Yamabe solitons

In this offering exposition, we intend to study paracontact metric manifold M admitting almost Yamabe solitons. First, for a general paracontact metric manifold, it is proved that V is Killing if the vector field V is an infinitesimal contact transformation and that M is K-paracontact if V is collinear with Reeb vector field. Second, we proved that a K-paracontact manifold admitting a Yamabe gradient soliton is of constant curvature - 1 when n = 1 and for n > 1, 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 V is Killing when n > 1. Finally, we consider a paracontact metric (kappa,mu)-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.