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MURATHAN, CENGİZHAN

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MURATHAN

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CENGİZHAN

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Now showing 1 - 10 of 16
  • Publication
    (κ, μ, υ = const.)-contact metric manifolds with ξ(IM)=0
    (Springer Heidelberg, 2014-03-01) ; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Erken, İ. Küpeli; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; ABH-3658-2020
    We give a local classification of (kappa, mu, upsilon = const.)-contact metric manifold (M, phi, xi, eta, g) with kappa < 1 which satisfies the condition" the Boeckx invariant function I-M = 1-mu/2/root 1-kappa is constant along the integral curves of the characteristic vector field xi".
  • 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-8167-2020
    In 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
    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-8775-2021
    We 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-5172-2022
    This 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
    Almost cosympletic statistical manifolds
    (Natl Inquiry Services, 2020-02-01) Erken, İrem Küpeli; Murathan, Cengizhan; Yazla, Aziz; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; ABH-3658-2020
    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. 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.
  • 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-3658-2020
    Main interest of the present paper is to obtain the generalized Wintgen inequality for Legendrian submanifolds in almost Kenmotsu statistical manifolds.
  • 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-3939-2023
    In 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
    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-8167-2020
    In 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
    A study of wintgen like inequality for submanifolds in statistical warped product manifolds
    (Springer Basel Ag, 2018-08-01) Şahin, Bayram; Murathan, Cengizhan; MURATHAN, CENGİZHAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; ABH-3658-2020; ABE-8167-2020
    In this paper, we study statistical manifolds and their submanifolds. We first construct two new examples of statistical warped product manifolds and give a method how to construct Kenmotsu-like statistical manifold and cosymplectic-like statistical manifold based on the existence of Kaehler-like statistical manifold. Then we obtain the general Wintgen inequality for statistical submanifolds of statistical warped product manifolds.
  • 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-9622-2020
    The 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).