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Öğe A Generalized Wintgen Inequality for Legendrian Submanifolds in Almost Kenmotsu Statistical Manifolds(2019) Görünüş, Ruken; Erken, İrem Küpeli; Yazla, Aziz; Murathan, CengizhanMain interest of the present paper is to obtain the generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu statistical manifolds.Öğe A Neutral relation between metallic structure and almost quadratic ?-structure(2019) Gönül, Sinem; Erken, İrem Küpeli; Yayla, Aziz; Murathan, CengizhanIn this paper, we give a neutral relation between metallic structure and almost quadratic metric ?-structure. Considering N as a metallic Riemannian manifold, we show that the warped product manifold R ?f N has an almost quadratic metric ?-structure. We define Kenmotsu quadratic metric manifolds, which include cosymplectic quadratic manifolds when $\beta=0$. Then we give nice almost quadratic metric ?-structure examples. In the last section, we construct a quadratic ?-structure on the hypersurface $M^n$ of a locally metallic Riemannian manifold $M^{n+1}$Öğe A study of three-dimensional paracontact ((kappa)over-tilde, (mu)over-tilde, (nu)over-tilde)-spaces(World Scientific Publ Co Pte Ltd, 2017) Erken, İrem Küpeli; Murathan, CengizhanThis paper is a study of three-dimensional paracontact metric ((kappa) over tilde, (mu) over tilde, (nu) over tilde)-manifolds. Three-dimensional paracontact metric manifolds whose Reeb vector field xi is harmonic are characterized. We focus on some curvature properties by considering the class of paracontact metric ((kappa) over tilde, (mu) over tilde, (nu) over tilde)-manifolds under a condition which is given at Definition 3.1. We study properties of such manifolds according to the cases (kappa) over tilde > -1, (kappa) over tilde = -1, (kappa) over tilde < -1 and construct new examples of such manifolds for each case. We also show the existence of paracontact metric (-1, <(mu)over tilde> not equal 0, (nu) over tilde not equal 0) spaces with dimension greater than 3, such that (h) over tilde (2) = 0 but (h) over tilde not equal 0.Öğe Almost cosympletic statistical manifolds(Natl Inquiry Services Centre Pty Ltd, 2020) Erken, İrem Küpeli; Murathan, Cengizhan; Yazla, AzizThis 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. A characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves are proved. We also study curvature properties of an almost cosymplectic statistical manifold. Moreover, examples are constructed.Öğe Biharmonic Pseudo-Riemannian Submersions from 3-Manifolds(Univ Nis, Fac Sci Math, 2018) Erken, İrem Küpeli; Murathan, CengizhanWe classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form onto a surface.Öğe CLASSIFICATION OF THREE-DIMENSIONAL CONFORMALLY FLAT QUASI-PARA-SASAKIAN MANIFOLDS(Honam Mathematical Soc, 2019) Erken, İrem KüpeliThe aim of this paper is to study three-dimensional conformally flat quasi-para-Sasakian manifolds. First, the necessary and sufficient conditions are provided for three-dimensional quasi-para-Sasakian manifolds to be conformally flat. Next, a characterization of three-dimensional conformally flat quasi-para-Sasakian manifold is given. Finally, a method for constructing examples of three-dimensional conformally flat quasi-para-Sasakian manifolds is presented.Öğe Cotton Solitons on Three Dimensional Almost $(Kazım İLARSLAN, 2023) Erken, İrem Küpeli; Özkan, Mustafa; Savur, BüşraIn this paper, we study Cotton solitons on three-dimensional almost ?-paracosymplectic manifolds. We especially focus on threedimensional almost ?-paracosymplectic manifolds with harmonic vector field ? and characterize them for all possible types of operator h. Finally, we constructed an example which satisfies our results.Öğe Curvature Properties of Quasi-Para-Sasakian Manifolds(Int Electronic Journal Geometry, 2019) Erken, İrem KüpeliThe paper is devoted to study quasi-para-Sasakian manifolds. Basic properties of such manifolds are obtained and general curvature identities are investigated. Next it is proved that if M is a quasi-para-Sasakian manifold of constant curvature K. Then K <= 0 and (z) if K = 0, the manifold is paracosymplectic, (ii) if K < 0, the quasi-para-Sasakian structure of M is obtained by a homothetic deformation of a para-Sasakian structure. Finally, an example of a 3-dimensional proper quasi-para-Sasakian manifold is constructed.Öğe Invariant Submanifolds of Paracontact Metric ((kappa)over-tilde not equal-1, (mu)over-tilde)-Manifolds(Springer Basel Ag, 2020) Erken, İrem KüpeliThe principal objective of this paper is to answer positively the open question whether every invariant submanifold of a paracontact metric ((kappa) over tilde, (mu) over tilde)-manifold is totally geodesic. Main result is that any invariant submanifold of a paracontact metric ((kappa) over tilde, (mu) over tilde)-manifold, (kappa) over tilde not equal -1, is always totally geodesic. Additionally, if (kappa) over tilde not equal - 1 and (mu) over tilde not equal 0 the result can be partially reversed, which shows that the totally geodesic submanifold is invariant under the flow of characteristic vector field is tangent to the submanifold.Öğe ON A CLASSIFICATION OF ALMOST ?-COSYMPLECTIC MANIFOLDS(Tusi Mathematical Research Group (TMRG), 2019) Erken, İrem KüpeliThe object of the present paper is to study almost ?-cosymplectic manifolds. We consider projectively flat, conformally flat, and concircularly flat almost ?-cosymplectic manifolds (with the ?-parallel tensor field ?h) and get some new properties. We conclude the paper by giving an example of ?-Kenmotsu manifold, which verifies our results. © 2019 khayyam journal of mathematics.Öğe PARACONTACT METRIC (?, µ) R-HARMONIC MANIFOLDS(Univ Kragujevac, Fac Science, 2020) Erken, İrem KüpeliWe give classifications of paracontact metric ((kappa) over tilde,(mu) over tilde) manifolds M2n+1 with harmonic curvature for n > 1 and n = 1.Öğe Reeb Flow Symmetry on 3-Dimensional Almost Paracosymplectic Manifolds(Univ Nis, Fac Sci Math, 2019) Erken, İrem KüpeliMainly, we prove that the Ricci operator Q of an 3-dimensional almost paracosymplectic manifold M is invariant along the Reeb flow, that is M satisfies L(xi)Q = 0 if and only if M is an almost paracosymplectic kappa-manifold with kappa not equal -1.Öğe Ricci collineations on 3-dimensional paracontact metric manifolds(Springer Heidelberg, 2018) Erken, İrem Küpeli; Murathan, C.We classify three-dimensional paracontact metric manifold whose Ricci operator Q is invariant along Reeb vector field, that is, L(xi)Q = 0.Öğe Riemannian Warped Product Submersions(Springer Basel Ag, 2021) Erken, İrem Küpeli; Murathan, CengizhanIn this paper, we introduce Riemannian warped product submersions and construct examples and give fundamental geometric properties of such submersions. On the other hand, a necessary and sufficient condition for a Riemannian warped product submersion to be totally geodesic, totally umbilic and minimal is given.
