Yamabe solitons on three-dimensional normal almost paracontact metric manifolds
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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 prove that either the manifold has constant curvature \(-\,1\) 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 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 \(\lambda =-6\).
KeywordsPara-Sasakian manifold Paracosymplectic manifold Para-Kenmotsu manifold Yamabe soliton Ricci soliton Infinitesimal automorphism Constant scalar curvature
Mathematics Subject Classification53C25 53C21 53C44 53D15
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