Yazar "Ilarslan, Kazim" seçeneğine göre listele

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    An application of Ritt-Wu's zero decomposition algorithm to null Bertrand type curves in Minkowski 3-space
    (Hacettepe Univ, Fac Sci, 2010) Yildirim, Mehmet; Ilarslan, Kazim
    Bertrand curves were first studied using a computer by W. -T. Wu in (A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585-588, 1987). The same problem was studied using an improved version of Ritt-Wu's decomposition algorithm by S. -C. Chao and X.-S. Gao (Automated reasoning in differential geometry and mechanics: Part 4: Bertrand curves, System Sciences and Mathematical Sciences 6(2), 186-192, 1993). In this paper, we investigate the same problem for null Bertrand type curves in Minkowski 3-space E-1(3) by using the well known algorithm given by Chao and Gao, and obtain new results for null Bertrand type curves in Minkowski 3-space E-1(3).
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    An application of Ritt-Wu's zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space
    (Springer Heidelberg, 2011) Ilarslan, Kazim; Yildirim, Mehmet
    The Bertrand curves were first studied using a computer by Wu (1987). The same problem was studied using an improved version of Ritt-Wu's decomposition algorithm by Chou and Gao (1993). This paper investigates the same problem for pseudo null Bertrand curves in Minkowski 3-space E1(3.)
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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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    Characterizations of the position vector of a surface curve in Euclidean 3-space
    (Ovidius Univ Press, 2011) Camci, Cetin; Kula, Levent; Ilarslan, Kazim
    In this paper, we give some characterizations of position vector of a unit speed curve in a regular surface M subset of E-3 which always lies in the planes spanned by {T, Z}, {T, Y} and {Y, Z}, respectively, by using (curve-surface)-frame {T,Y,Z} instead of Frenet frame {T, N, B}. We characterize such curves in terms of the geodesic curvature k(g), normal curvature k(n) and geodesic torsion t(r). Furthermore, we give some characterization for the regular surface M by using the concept of transversality of surfaces in Euclidean 3-space.
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    Characterizations of timelike slant helices in Minkowski 3-space
    (Univ Osijek, Dept Mathematics, 2014) Gok, Ismail; Nurkan, Semra Kaya; Ilarslan, Kazim; Kula, Levent; Altinok, Mesut
    In this paper, we investigate the tangent indicatrix, the principal normal indicatrix and the binormal indicatrix of a timelike curve in Minkowski 3-space E-1(3) and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize a timelike curve to be a slant helix by using the Frenet apparatus of a spherical indicatrix of the curve. Also, related examples and their illustrations are given.
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    Differential Geometry From a Singularity Theory Viewpoint
    (Inst Biophysics & Biomedical Engineering, Bulgarian Acad Sciences, 2016) Ilarslan, Kazim
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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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    Frenet Curves in Euclidean 4-Space
    (Int Electronic Journal Geometry, 2017) Deshmukh, Sharief; Al-Dayel, Ibrahim; Ilarslan, Kazim
    In this paper, we study rectifying curves arising through the dilation of unit speed curves on the unit sphere S-3 and conclude that arcs of great circles on S-3 do not dilate to rectifying curves, which develope previously obtained results for rectifying curves in Eucidean spaces. This fact allows us to prove that there exists an associated rectifying curve for each Frenet curve in the Euclidean space E-4 and a result of the fact rectifying curves in the Euclidean space E-4 are ample, indeed as an appication, we present an ordinary differential equation satisfied by the distance function of a Frenet curve in E-4 which alows us to characterize the spherical curves and rectifying curves in E-4. Furthermore, we study ccr-curves in the Euclidean space E-4 which are generalizations of helices in E-3 and show that the property of a helix that its tangent vector field makes a constant angel with a fixed vector (axis of helix) does not go through for a ccr-curve.
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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 spacelike slope axis in Minkowski 3-space
    (World Scientific Publ Co Pte Ltd, 2019) Ucum, Ad; Camci, Cetin; Ilarslan, Kazim
    In the present paper, we consider general helix with spacelike slope axis for all possible types of curves in Minkowski 3-space. We give the conditions under which the curves in Minkowski 3-space have spacelike slope axis. In addition, we find the parametric equations of the curves. Also, we give the related examples and their graphics.
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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 Null Bertrand Curves In Minkowski Space-Time
    (Univ Al I Cuza, Fac Math, 2014) Aksoyak, Ferdag Kahraman; Gok, Ismail; Ilarslan, Kazim
    COKEN and CIFTCI proved that a null Cartan curve in Minkowski space-time E-1(4) is a null Bertrand curve if and only if k(2) is nonzero constant and k(3) is zero. That is, the null curve with non-zero curvature k(3) is not a Bertrand curve in Minkowski space-time E-1(4). So, in this paper we defined a new type of Bertrand curve in Minkowski space-time El for a null curve with non-zero curvature k(3) by using the similar idea of generalized Bertrand curve given by MATSUDA and YOROZU and we called it a null (1, 3)-Bertrand curve. Also, we proved that if a null curve with non-zero curvatures in Minkowski spacetime E-1(4) is a null (1, 3)-Bertrand curve then it is a null helix. We give an example of such curves.
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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).