Person: MURATHAN, CENGİZHAN
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MURATHAN
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CENGİZHAN
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Publication A generalized wintgen inequality for legendrian submanifolds in almost kenmotsu statistical manifolds(Int Electronic Journal Geometry, 2019-04-01) Görünüş, Ruken; Erken, İrem Küpeli; Yazla, Aziz; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/ Matematik Bölümü; ABE-8167-2020; ABH-3658-2020Main interest of the present paper is to obtain the generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu statistical manifolds.Publication Riemannian warped product submersions(Springer, 2021-03-01) Erken, İrem Küpeli; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-2273-3243; ABE-8167-2020In 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.Publication The Chen's first inequality for submanifolds of statistical warped product manifolds(Elsevier, 2021-06-27) Siddiqui, Aliya Naaz; Murathan, Cengizhan; Siddiqi, Mohd Danish; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; ABE-8167-2020The study of warped products plays versatile roles in differential geometry as well as in mathematical physics, especially in general relativity (GR). In the present paper, we study statistical submanifolds in a statistical warped product with some related examples. For such submanifolds, we establish a Chen's first inequality and also discuss the equality case. Finally, we study the statistical warped product immersions and obtain some results.Publication The curvature tensor of -contact metric manifolds(Springer, 2015-07-01) Arslan, Kadri; Carriazo, Alfonso; Martin-Molina, Veronica; Murathan, Cengizhan; ARSLAN, KADRİ; MURATHAN, CENGİZHAN; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; ABE-8167-2020; ABH-3658-2020; AAG-8775-2021We study the Riemann curvature tensor of -contact metric manifolds, which we prove to be completely determined in dimension 3. We also observe how this curvature tensor is affected by -homothetic deformations, which will prompt the definition and study of generalized -space forms and of the necessary and sufficient conditions for them to be conformally flat.Publication Almost α-paracosymplectic manifolds(Elsevier, 2015-02-01) Küpeli, Erken; Dacko, P.; Murathan, Cengiz; Küpeli, Erken; Dacko, P.; MURATHAN, CENGİZHAN; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-3054-8213; ABH-3658-2020; ETS-4402-2022; ESL-5172-2022This paper is a complete study of almost alpha-paracosymplectic manifolds. Basic properties of such manifolds are obtained and general curvature identities are proved. The manifolds with para-Kaehler leaves are characterized. It is proved that, for dimensions greater than 3, almost alpha-paracosymplectic manifolds are locally conformal to almost paracosymplectic manifolds and locally D-homothetic to almost para-Kenmotsu manifolds. Furthermore, it is proved that characteristic (Reeb) vector field xi is harmonic on almost alpha-para-Kenmotsu manifold if and only if it is an eigenvector of the Ricci operator. It is showed that almost alpha-para-Kenmotsu (kappa, mu, nu)-space has para-Kaehler leaves. 3-dimensional almost alpha-para-Kenmotsu manifolds are classified. As an application, it is obtained that 3-dimensional almost alpha-para-Kenmotsu manifold is (kappa, mu, nu)-space on an every open and dense subset of the manifold if and only if Reeb vector field is harmonic. Furthermore, examples are constructed.Publication A class of lorentzian α-sasakian manifolds(Kyungpook Natl Univ, Dept Mathematics, 2009-12-01) Yıldız, Ahmet; Turan, Mine; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-9799-1781; ABE-8167-2020; ABH-3658-2020; HSF-3939-2023In this study we consider phi-conformally flat, phi-conharmonically flat, phi-projectively flat and f concircularly flat Lorentzian alpha-Sasakian manifolds. In all cases, we get the manifold will be an eta-Einstein manifold.Publication Cotton solitons on three dimensional paracontact metric manifolds(Univ Nis, 2023-01-01) Özkan, Mustafa; Erken, İrem Küpeli; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; ABE-8167-2020In 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.Publication On lorentzian α-sasakian manifolds(Kyungpook Natl Univ, Dept Mathematics, 2005-03-01) Yıldız, Ahmet; Murathan, Cengizhan; MURATHAN, CENGİZHAN; 0000-0002-9799-1781; ABE-8167-2020; ABH-3658-2020; HSF-3939-2023; ABG-9622-2020The present paper deals with Lorentzian alpha-Sasakian manifolds with conformally flat and quasi conformally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere S-2n + 1 (c). Further it is shown that an Lorentzian alpha-Sasakian manifold with R (X; Y):C = 0 is locally isometric with a sphere S-2n + 1 (c), where c = alpha(2).Publication Ricci collineations on 3-dimensional paracontact metric manifolds(Springer, 2018-06-01) Erken, L. Küpeli; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; ABE-8167-2020We classify three-dimensional paracontact metric manifold whose Ricci operator Q is invariant along Reeb vector field, that is, L(xi)Q = 0.Publication Invariant submanifolds of sasakian space forms(Springer Basel Ag, 2009-11-01) Yıldız, Ahmet; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi.; 0000-0002-9799-1781; ABE-8167-2020In the present study, we consider isometric immersions f : M -> M (c) of (2n + 1)-dimensional invariant submanifold M2n+ 1 of (2m+ 1)dimensional Sasakian space form M (2m+ 1) of constant phi-sectional curvature c. We have shown that if f satisfies the curvature condition (R) over bar (X, Y) sigma = Q(g, sigma) then either M2n+ 1 is totally geodesic, or parallel to sigma parallel to(2) = 1/3 (2c+ n(c+ 1)), or parallel to sigma parallel to(2) (x) > 1/3 (2c + n(c + 1) at some point x of M2n+ 1. We also prove that R(X, Y).sigma = 1/2n Q(S, sigma) then either M2n+ 1 is totally geodesic, or parallel to sigma parallel to(2) = - 2/3 (1/2n T - 1/2 (n + 2)(c + 3) + 3), or parallel to sigma parallel to(2) (x) > - 2/3 (1/2n T (x) 1/2 (n + 2)(c + 3) + 3) at some point x of M2n+1.