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ARSLAN, KADRİ

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Now showing 1 - 10 of 22
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    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; 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.
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    Publication
    Focal representation of k-slant helices in Em+1
    (De Gruyter Poland Sp Zoo, 2015-12-01) Öztürk, Günay; Bayram, Bengü; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-8775-2021; AAG-7693-2021
    The focal representation of a generic regular curve gamma in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix gamma in Em+1 is a (generic) regular curve whose unit normal vector V-k makes a constant angle with a fixed direction (U) over right arrow in Em+1. In the present paper we proved that if gamma is a k-slant helix in Em+1, then the focal representation C-gamma of gamma in Em+1 is an (m - k + 2)-slant helix in Em+1.
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    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; 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)
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    Publication
    General rotational surfaces satisfying ΔxT = φxT
    (Springer Basel Ag, 2022-02-01) Demirbaş, Eray; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0001-5861-0184
    In the present study we consider rotational surfaces in Euclidean 4-space whose canonical vector field x(T) satisfy the equality Delta x(T) = phi x(T). Further, we obtain some results related to three types of general rotational surfaces in E-4 satisfying this equality. We also give some examples related with these type of surfaces.
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    Publication
    On translation surfaces in 4-dimensional euclidean space
    (Univ Tartu Press, 2016-12-01) Bayram, Bengü; Öztürk, Günay; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betul; BULCA SOKUR, BETÜL; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-1440-7050; 0000-0001-5861-0184; AAG-8775-2021; AAG-7693-2021
    We consider translation surfaces in Euclidean spaces. Firstly, we give some results of translation surfaces in the 3-dimensional Euclidean space E-3. Further, we consider translation surfaces in the 4-dimensional Euclidean space E-4. We prove that a translation surface is flat in E-4 if and only if it is either a hyperplane or a hypercylinder. Finally we give necessary and sufficient condition for a quadratic triangular Bezier surface in E-4 to become a translation surface.
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    Publication
    Surface pencils in euclidean 4-space e 4
    (World Scientific Publ Co Pte Ltd, 2016-12-01) Bulca, Betül; BULCA SOKUR, BETÜL; Arslan, Kadri; ARSLAN, KADRİ; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-8775-2021; AAG-7693-2021
    In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in 4-dimensional Euclidean space E-4. We have shown that the generalized rotation surfaces in E-4 are the special type of surface pencils. Further, the curvature properties of these surfaces are investigated. Finally, we give some examples of flat surface pencils in E-4.
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    Publication
    Biminimal curves in euclidean spaces
    (Int Electronic Journal Geometry, 2009-10-01) Öztürk, Günay; Ugail, Hassan; ARSLAN, KADRİ; Aydın, Yılmaz; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-1440-7050; 0000-0002-3084-1797; AAG-8775-2021
    We study with biminimal curves, that is curves which are critical points of the bienergy for normal variations. We give a description of the Euler-Lagrange equation associated to biminimal curves on a Riemannian manifold. We describe curves of AW(k) type of Euclidean n-space E-n. We show that every biminimal curves of E-n are of AW(1)-type. We also show that lambda-biminimal curves of E-n are of AW(3)-type.
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    Publication
    On generalized spherical surfaces in euclidean spaces
    (Honam Mathematical Soc, 2017-09-01) Bayram, Bengü; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-1440-7050; 0000-0001-5861-0184; AAG-7693-2021
    In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1) space En+1. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces E-3 and E-4 respectively. We have shown that the generalized spherical surfaces of first kind in E-4 are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in I. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.
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    Publication
    On tzitzeica curves in euclidean 3-space e 3
    (Univ Nis, 2018-01-01) Bayram, Bengü; Tunc, Emrah; Öztürk, Günay; Arslan, Kadri; ARSLAN, KADRİ; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; AAG-8775-2021
    In this study, we consider Tzitzeica curves (Tz-curves) in a Euclidean 3-space E-3. We characterize such curves according to their curvatures. We show that there is no Tz-curve with constant curvatures (W-curves). We consider Salkowski (TC-curve) and anti-Salkowski curves.
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    Publication
    Semi-parallel meridian surfaces in E⁴
    (Int Electronic Journal Geometry, 2015-10-01) Bulca, Betül; Arslan, Kadri; BULCA SOKUR, BETÜL; ARSLAN, KADRİ; Ulıdağ Üniversitesi; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-7693-2021; AAG-8775-2021
    In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We classify semi-parallel meridian surfaces in 4-dimensional Euclidean space E-4.