Searcharxiv⌕ Search

arXiv subjects

Cengizhan Murathan

Publications and source records attributed to Cengizhan Murathan.

12 recordsLinked to original sources
arXiv2020

B.-Y. Chen's inequality for $CR$-warped products in a locally conformal Kaehler space form

n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for the important subclass of locally conformal Kaehler manifolds i.e., Vaisman manifold.

math.DG↗
arXiv2018

A neutral relation between metallic structure and almost quadratic ϕ-structure

In this paper, metallic structure and almost quadratic metric phi-structure are studied. Based on metallic (polynomial) Riemannian manifold, Kenmotsu quadratic metric manifold, cosymplectic quadratic metric manifold are defined and gave some examples. Finally, we construct quadratic phi-structure on the hypersurface M^n of a locally metallic Riemannian manifold M^n+1.

math.GM↗
arXiv2018

Almost cosymplectic statistical manifolds

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves. We also study curvature properties of an almost cosymplectic statistical manifold. Moreover, examples are constructed.

math.DG↗
arXiv2017

A Study of Three-Dimensional Paracontact $(κ,μ,ν) $-SPACES

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.

math.DG↗
arXiv2015

On the existence of proper Nearly Kenmotsu manifolds

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.

math.DG↗
arXiv2013

On Slant Riemannian Submersions For Cosymplectic Manifolds

In this paper we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifolds. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions according to characteristic vector field is vertical or horizontal.

math.DG↗
arXiv2012

(κ,μ,\u{psion}=const.)-Contact Metric Manifolds With ξ(I_{M})=0

We give a local classification of (κ,μ,\u{psion}=const.)-contact metric manifold (M,ϕ,ξ,η,g) with κ<1 which satisfies the condition" the Boeckx invariant function I_{M}=((1-(μ/2))/(\surd(1-κ))) is constant along the integral curves of the characteristic vector field ξ".

math.DG↗
arXiv2011

The curvature tensor of (\ka,μ,ν)-contact metric manifolds

We study the Riemann curvature tensor of (κ,μ,ν)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (κ,μ,ν)-space forms and of the necessary and sufficient conditions for them to be conformally flat.

math.DG↗
arXiv2010

Almost α-Cosymplectic (κ,μ,ν)-Spaces

Main interest of the present paper is to investigate the almost α-cosymplectic manifolds for which the characteristic vector field of the almost α-cosymplectic structure satisfies a specific (κ,μ,ν)-nullity condition. This condition is invariant under D-homothetic deformation of the almost cosymplectic (κ,μ,ν)-spaces in all dimensions. Also, we prove that for dimensions greater than three, κ,μ,ν are not necessary constant smooth functions such that df^η=0. Then the existence of the three-dimensional case of almost cosymplectic (κ,μ,ν)-spaces are studied. Finally, we construct an appropriate example of such manifolds.

math.DG↗