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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 Cotton solitons on three dimensional paracontact metric manifolds(Univ Nis, Fac Sci Math, 2023) Ozkan, Mustafa; Erken, Irem Kupeli; Murathan, CengizhanIn this paper, we study Cotton solitons on three-dimensional paracontact metric manifolds. We especially focus on three-dimensional paracontact metric manifolds with harmonic vector field xi and characterize them for all possible types of operator h. Finally, we constructed an example which satisfies our results.Öğe Inequalities on Riemannian Warped Product Submersions for Vertical Casorati Curvatures(Springer Basel Ag, 2023) Erken, Irem Kupeli; Murathan, Cengizhan; Siddiqui, Aliya NaazThe first and second authors introduced Riemannian warped product submersions and discussed interesting fundamental geometric properties of such submersions in Kupeli Erken and Murathan,. In the present paper, we extend this study to put light on the curvature properties of such submersions and then obtain optimal inequalities for Riemannian warped product submersions involving vertical Casorati curvatures. Also, we discuss under which conditions the equality case of inequality can hold with an example.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.
