Geometry of paracontact metric as an almost Yamabe solitons
Abstract
In this offering exposition, we intend to study paracontact metric manifold MM admitting almost Yamabe solitons. First, for a general paracontact metric manifold, it is proved that VV is Killing if the vector field VV is an infinitesimal contact transformation and that MM is KK-paracontact if VV is collinear with Reeb vector field. Second, we proved that a KK-paracontact manifold admitting a Yamabe gradient soliton is of constant curvature −1−1 when n=1n=1 and for n>1n>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 VV is Killing when n>1n>1. Finally, we consider a paracontact metric (κ,μ)(κ,μ)-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.
