arXiv subjects
Publications and source records attributed to Irem Kupeli Erken.
The object of the present paper is to study 3-dimensional conformally flat quasi-Para-Sasakian manifolds. First, the necessary and sufficient conditions are provided for 3-dimensional quasi-Para-Sasakian manifolds to be conformally flat. Next, a characterization of 3-dimensional conformally flat quasi-Para-Sasakian manifold with \b{eta}=const. is given.
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.
This paper is a study of three-dimensional paracontact metric (\k{appa},μ,ν)-manifolds. Three dimensional paracontact metric manifolds whose Reeb vector field ξ is harmonic are characterized. We focus on some curvature properties by considering the class of paracontact metric (\k{appa},μ,ν)-manifolds under a condition which is given at Definition 3.1. We study properties of such manifolds according to the cases \k{appa}>-1, \k{appa}=-1, \k{appa}<-1 and construct new examples of such manifolds for each case.
This is an expository paper, which provides a first approach to nearly Kenmotsu manifolds. The purpose of this paper is to focus on nearly Kenmotsu manifolds and get some new results from it. We prove that for a nearly Kenmotsu manifold is locally isometric to warped product of real line and nearly Kähler manifold. Finally, we prove that there exist no nearly Kenmotsu hypersurface of nearly Kähler manifold. It is shown that a normal nearly Kenmotsu manifold is Kenmotsu manifold.
We give a local classification of generalized (kappa,mu)-Paracontact Metric Manifold which satisfies the condition xi(mu)=0. An example of such manifolds is presented.