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Yamabe solitons on three-dimensional normal almost paracontact metric manifolds

  • Irem Küpeli ErkenEmail author
Article
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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 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 \(\lambda =-6\).

Finally, we construct examples to illustrate the results obtained in previous sections.

Keywords

Para-Sasakian manifold Paracosymplectic manifold Para-Kenmotsu manifold Yamabe soliton Ricci soliton Infinitesimal automorphism Constant scalar curvature 

Mathematics Subject Classification

53C25 53C21 53C44 53D15 

Notes

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Engineering and Natural SciencesBursa Technical UniversityBursaTurkey

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