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 prove that the following: 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 is Killing. In the next step, we prove that either the manifold has constant curvature - or 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 the 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. Furthermore, Yamabe soliton is expanding with lambda=-6. Finally, we construct examples to illustrate the results obtained in previous sections.