Person:
ARSLAN, KADRİ

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ARSLAN

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KADRİ

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Now showing 1 - 10 of 18
  • Publication
    Rotational surfaces with rotations in x3x4-plane
    (Tsing Hua Univ, Dept Mathematics, 2021-01-01) Arslan, Kadri; Bulca, Betül; ARSLAN, KADRİ; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0001-5861-0184; EJT-1458-2022; AAG-7693-2021
    In the present study we consider generalized rotational surfaces in Euclidean 4-space E-4. Further, we obtain some curvature properties of these surfaces. We also introduce some kind of generalized rotational surfaces in E-4 with the choice of meridian curve. Finally, we give some examples.
  • Publication
    A new characterization of curves in minkowski 4-SPACE E 1 4
    (Univ Nis, 2020-01-01) Kisi, Ilim; Öztürk, Günay; Arslan, Kadri; ARSLAN, KADRİ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAG-8775-2021
    In this study, we attend to the curves whose position vectors are written as a linear combination of their Serret-Frenet vectors in Minkowski 4-space E-1(4). We characterize such curves with regard to their curvatures. Further, we get certain consequences of T-constant and N-constant types of curves in E-1(4).
  • Publication
    General rotational ξ-surfaces in euclidean spaces
    (Tubitak Scientific & Technological Research Council Turkey, 2021-01-01) Arslan, Kadri; ARSLAN, KADRİ; Aydın, Yılmaz; Bulca, Betul; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184
    The general rotational surfaces in the Euclidean 4-space R-4 was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, xi-surfaces are the generalization of self-shrinker surfaces. In the present article we consider xi-surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean xi- space R-4 to become self-shrinkers. Furthermore, we classify the general rotational xi-surfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational xi-surfaces in R-4.
  • 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
    A characterization of involutes and evolutes of a given curve in En
    (Kyungpook Natl Univ, Dept Mathematics, 2018-03-01) Öztürk, Günay; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; 0000-0001-5861-0184; AAG-8775-2021; AAG-7693-2021
    The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space E-n. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space E-n. Further, we obtain some results on these type of curves in E-3 and E-4, respectively.
  • Publication
    Characterizations of space curves with 1-type darboux instantaneous rotation vector
    (Korean Mathematical Soc, 2016-01-01) Kocayiğit, Hüseyin; Önder, Mehmet; Arslan, Kadri; ARSLAN, KADRİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; AAG-8775-2021
    In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space E-3. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.
  • Publication
    Some characterizations of timelike and spacelike curves with harmonic 1-type darboux instantaneous rotation vector in the minkowski 3-space E13
    (Ankara Univ, Fac Sci, 2013-01-01) Kocayiğit, Hüseyin; Önder, Mehmet; Arslan, Kadri; ARSLAN, KADRİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/ Matematik Bölümü.; 0000-0002-1440-7050; AAG-8775-2021
    In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E-1(3)
  • Publication
    Tangentially cubic submanifolds of Em
    (Int Electronic Journal Geometry, 2010-10-01) Öztürk, Günay; Bayram, Bengü Kılıç; Arslan, Kadri; ARSLAN, KADRİ; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAG-8775-2021
    In the present study we consider the submanifold M of E-m satisfying the condition Delta H, e(i) = 0, where H is the mean curvature of M and e(i) is an element of TM. We call such submanifolds tangentially cubic. We proved that every null 2- type submanifold M of E-m is tangentially cubic. Further, we prove that the pointed helical geodesic surfaces of E-5 with constant Gaussian curvature are tangentially cubic.
  • Publication
    Curves of generalized aw ( k )-type in euclidean spaces
    (Int Electronic Journal Geometry, 2014-10-01) Güvenç, Şaban; Arslan, Kadri; ARSLAN, KADRİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-1440-7050; AAG-8775-2021
    In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.
  • Publication
    On constant-ratio surfaces of rotation in euclidean 4-space
    (World Scientific Publ Co Pte Ltd, 2023-09-27) Arslan, Kadri; Bulca, Betül; Demirbaş, Eray; ARSLAN, KADRİ; BULCA SOKUR, BETÜL; Demirbaş, Eray; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; EJT-1458-2022; AAG-7693-2021; ESA-0181-2022
    The general rotational surfaces of E-4 were first studied by Moore. The Vranceanu surfaces are special examples of this kind of surfaces. These constant-ratio surfaces are surfaces for which the ratio of the norms of the tangent and normal components of the position vector fields is constant. However, spherical surfaces and conical surfaces are also trivial examples of constant-ratio surfaces. Thus, if the norms of the tangent or normal components of the position vector fields are constant, then the given surface is called T-constant or N-constant, respectively. In this paper, we considered three types of rotational surfaces lying in 4-dimensional Euclidean space E-4. We have obtained the necessary and sufficient conditions for these surfaces to satisfy the T-constant, N-constant or constantratio conditions. With the help of these results, we characterized the meridian curves of the surfaces. Further, we also give some examples to support the results obtained.