2017/08/14 by İrem Küpeli Erken, Erken, Irem Kupeli · 1 citation
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1708.04882
openalex publication_date 2017/08/14 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28
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 η-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 λ=-6 and the vector field V is Killing. Finally, we construct examples to illustrate the results obtained in previous sections.