Yazar "Ucum, Ali" seçeneğine göre listele

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    Bi-null curves with constant curvatures in R-2(5)
    (Springer Basel Ag, 2019) Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim
    In the present paper, we classify bi-null curves with constant curvatures in semi-Euclidean 5-space R-2(5) with index 2.
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    Elastic Sturmian spirals in the Lorentz-Minkowski plane
    (De Gruyter Poland Sp Zoo, 2016) Ucum, Ali; Ilarslan, Kazim; Mladenov, Ivailo M.
    In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form. We study in more details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.
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    General Helices with Lightlike Slope Axis
    (Univ Nis, Fac Sci Math, 2018) Camci, Cetin; Ilarslan, Kazim; Ucum, Ali
    In this paper, we investigate general helices with lightlike slope axis. We give necessary and sufficient conditions for a general helix to have a lightlike slope axis. We obtain parametric equation of all general helices with lightlike slope axis. Also we give a nice relation between helix with lightlike slope axis and biharmonic curves in Minkowski 3-space E-1(3).
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    General Helices with Timelike Slope Axis in Minkowski 3-Space
    (Springer Basel Ag, 2016) Ucum, Ali; Camci, Cetin; Ilarslan, Kazim
    In the present paper, we consider the general helices in Minkowski 3-space to have a constant timelike slope axis. As a result, we show that there exists no pseudo null helix with constant timelike slope axis or spacelike helix with timelike principal normal and constant timelike slope axis. Moreover, we obtain the parametric equations of spacelike helix with spacelike principal normal, timelike helix and null Cartan helix with timelike slope axis. We also give some related examples and their figures.
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    Generalized Bertrand Curves with Spacelike (1,3)-Normal Plane in Minkowski Space-Time
    (Scientific Technical Research Council Turkey-Tubitak, 2016) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we reconsider the (1, 3)-Bertrand curves with respect to the casual characters of a (1, 3)-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of (1, 3)-Bertrand curves to the spacelike (1, 3)-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike (1, 3)-normal plane to be (1, 3)-Bertrand curves and we give the related examples for these curves.
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    Generalized Bertrand curves with timelike (1,3)-normal plane in Minkowski space-time
    (Academic Publication Council, 2015) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we reconsider the (1,3)-Bertrand curves with respect to the casual characters of (1,3)-normal plane which is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of (1,3)-Bertrand curves to the timelike (1,3)-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with timelike (1,3)-normal plane to be (1,3)-Bertrand curves and we give the related examples for these curves.
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    Generalized Helicoidal Surfaces in Euclidean 5-space
    (Ovidius Univ Press, 2021) Ucum, Ali; Sakaki, Makoto
    In this paper, we study generalized helicoidal surfaces in Euclidean 5 space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.
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    Generalized pseudo null Bertrand curves in semi-Euclidean 4-space with index 2
    (Springer-Verlag Italia Srl, 2016) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we study generalized pseudo null Bertrand curves in semi-Euclidean 4-space E-2(4) with index 2. We get the necessary and sufficient conditions for pseudo null curves to be generalized Bertrand curves and we give some examples.
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    k-Type Bi-null Cartan Slant Helices in R-3(6)
    (Southeast Asian Mathematical Soc-Seams, 2018) Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto
    In the present paper, we give the notion of k-type bi-null Cartan slant helices in R-3(6), where k ( )is an element of {1, 2, 3, 4, 5, 6}. We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions.
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    k-TYPE BI-NULL CARTAN SLANT HELICES IN R26
    (Univ Kragujevac, Fac Science, 2022) Ucum, Ali; Ilarslan, Kazim
    In the present paper, we give the notion of k-type bi-null Cartan slant helices in R-2(6), where k is an element of{1, 2, 3, 4, 5, 6}. We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions.
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    k-Type bi-null slant helices in R-2(5)
    (Springer Basel Ag, 2017) Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto
    In the present paper, we give the notion of k-type bi-null slant helices in R-2(5), where k is an element of {0, 1, 2, 3, 4}. We give the necessary and sufficient conditions for bi-null curves to be k-type slant helices in terms of their curvature functions.
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    k-Type Hyperbolic Slant Helices in H3
    (Univ Nis, Fac Sci Math, 2020) Ucum, Ali; Ilarslan, Kazim
    In the present paper, we give the notion of k-type hyperbolic slant helices in H-3, where k is an element of {0, 1, 2, 3}. We give the necessary and sufficient conditions for hyperbolic curves to be k-type slant helices in terms of their hyperbolic curvature functions.
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    Lorentzian stationary surfaces and bi-null curves in R-2(5)
    (World Scientific Publ Co Pte Ltd, 2017) Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim
    In this paper, we study Lorentzian stationary surfaces related to bi-null curves in R-2(5). Considering a Gauss-like map, we get Lorentzian stationary surfaces and marginally trapped surfaces in the pseudo-sphere S-2(4) (1).
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    A new approach to Bertrand curves in Euclidean 3-space
    (SPRINGER BASEL AG, 2020) Camci, Cetin; Ucum, Ali; Ilarslan, Kazim
    In this article, a new approach is given for Bertrand curves in 3-dimensional Euclidean space. According to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Bertrand curve in E-3. In addition, the related examples and graphs are given by showing that general helices and anti-Salkowski curves can be Bertrand curves or their mates, which is their new characterization.
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    New Types of Canal Surfaces in Minkowski 3-Space
    (Springer Basel Ag, 2016) Ucum, Ali; Ilarslan, Kazim
    Canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. In Minkowski 3-space, many authors studied canal surfaces. However, when one investigates the papers, it is obvious that the parametrizations of the canal surfaces were found with respect to only pseudo sphere . In this paper, we reconsider the canal surfaces for all Lorentz spheres which are pseudo sphere , pseudo-hyperbolic sphere H (2)(r) or lightlike cone C and we find the parametrizations of the surfaces. Moreover, we found the parametrization of the tubular surfaces with respect to all Lorentz spheres. Also, we study Weingarten and linear Weingarten type spacelike tubular surface obtained from pseudo-hyperbolic sphere and the singular points of the spacelike tubular surface obtained from pseudo-hyperbolic sphere H-0(2)(r).
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    Note On Bertrand B-Pairs Of Curves In Minkowski 3-Space
    (Honam Mathematical Soc, 2018) Ilarslan, Kazim; Ucum, Ali; Aslan, Nihal Kilic; Nesovic, Emilija
    In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space ET according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.
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    On (1, 3)-Cartan null Bertrand curves in semi-Euclidean 4-space with index 2
    (Springer Basel Ag, 2016) Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto
    In this paper, we study generalized Cartan null Bertrand curves in semi-Euclidean 4-space E-2(4) with index 2.
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    On bi-null Cartan curves in semi-Euclidean 6-space with index 3
    (Springer Basel Ag, 2016) Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim
    In this paper, we study bi-null curves in semi-Euclidean 6-space with index 3, R-3(6). We construct the Frenet frame and Cartan curvature functions of bi-null curves in R-3(6). Also we discuss some properties of bi-null Cartan curves in terms of the Cartan curvatures.
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    On Generalized Spacelike Mannheim Curves in Minkowski Space-Time
    (Natl Acad Sciences India, 2016) Ilarslan, Kazim; Ucum, Ali; Nesovic, Emilija
    In this paper, by taking consideration of all possible causal characters of the plane spanned by {B-1*; B-2* }, we give the necessary and sufficient conditions for spacelike curves in E-1(4) to be generalized spacelike Mannheim curves in terms of their curvature functions.
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    On Generalized Timelike Mannheim Curves in Minkowski Space-time
    (Taylor & Francis Ltd, 2015) Ucum, Ali; Nesovic, Emilija; Ilarslan, Kazim
    In Minkowski space-time, timelike generalized Mannheim curves are studied by Akyigit and et al in [1]. In that paper, the authors take the Mannheim mate alpha* of the timelike curve a as a timelike curve in Minkowski space-time E-1(4). In this statement, the plane spanned by {B-1*, B-2*} becomes a spacelike plane. Thus the other possible cases such as timelike and null for the plane spanned by {B-1*, B-2*} is not considered. In this paper, by taking consideration of all possible causal characters of the plane spanned by{B-1*, B-2*}, we give the necessary and sufficient conditions for timelike curves ME to be generalized timelike Mannheim curves in terms of their curvature functions. Also, the related examples are given.