Yamabe Solitons on three-dimensional normal almost paracontact metric manifolds

Abstract

The purpose of the paper is to study Yamabe solitons on three-dimensional para-Sasakian, paracosymplectic and para-Kenmotsu manifolds. Mainly, we proved that *If the semi-Riemannian metric of a three-dimensional para-Sasakian manifold is a Yamabe soliton, then it is of constant scalar curvature, and the flow vector field V is Killing. In the next step, we proved that either manifold has constant curvature -1 and reduces to an Einstein manifold, or V is an infinitesimal automorphism of the paracontact metric structure on the manifold. *If the semi-Riemannian metric of a three-dimensional paracosymplectic manifold is a Yamabe soliton, then it has constant scalar curvature. Furthermore either manifold is $\eta$-Einstein, or Ricci flat. *If the semi-Riemannian metric on a three-dimensional para-Kenmotsu manifold is a Yamabe soliton, then the manifold is of constant sectional curvature -1, reduces to an Einstein manifold. Furthermore, Yamabe soliton is expanding with $\lambda$=-6 and the vector field V is Killing. Finally, we construct examples to illustrate the results obtained in previous sections.