Yazar "Nesovic, Emilija" seçeneğine göre listele

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    Numerical computing of isophote curves, general helices, and relatively normal-slant helices in Minkowski 3-space
    (Wiley, 2022) Öztürk, Ufuk; Nesovic, Emilija; Öztürk, Esra Betül Koç
    In this paper, we present a method for numerical computing of some characteristic kinds of non-null curves lying on a non-degenerate surface in Minkowski space 13. Namely, we obtain the system of the first-order ordinary differential equations that correspond to general helix, relatively normal-slant helix, and isophote curve and integrate it under chosen initial conditions by applying the ode45 function of MATLAB and Runge-Kutta method. Depending on the kind of curve, we assume that parametric equation of the surface, an axis vector, value of the real cosine or hyperbolic cosine of the corresponding pseudo angle between axis vector and Darboux frame's vector, normal curvature, and geodesic torsion of the curve are given. Finally, we provide the related examples of numerically computed characteristic curves.
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    On generalized Darboux frame of a spacelike curve lying on a lightlike surface in Minkowski space E31 Dedicated to the memory of Professor Emeritus Krishan Lal Duggal
    (Scientific and Technological Research Council Turkey, 2023) Djordjevic, Jelena; Nesovic, Emilija; Öztürk, Ufuk
    In this paper we introduce generalized Darboux frame of a spacelike curve alpha lying on a lightlike surface in Minkowski space E31 . We prove that alpha has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions kg, kn , tau g of alpha with respect to its Darboux frame and the curvature functions k similar to g, k similar to n , tau similar to g with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on which the tangent and the binormal indicatrix of a null Cartan curve are the principal curvature lines having tau similar to g = 0 and give some examples.
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    On non-null relatively normal-slant helices in minkowski 3-space
    (Univ Nis, Fac Sci Math, 2022) Nesovic, Emilija; Öztürk, Ufuk; Öztürk, Esra Betül Koç
    By using the Darboux frame {;xi, zeta, eta} of a non-null curve lying on a timelike surface in Minkowski 3-space, where xi is the unit tangent vector of the curve, eta is the unit spacelike normal vector field restricted to the curve and zeta = +/-eta x xi, we define relatively normal-slant helices as the curves satisfying the condition that the scalar product of the fixed vector spanning their axis and the non-constant vector field zeta is constant. We give the necessary and sufficient conditions for non-null curves lying on a timelike surface to be relatively normal-slant helices. We consider the special cases when non-null relatively-normal slant helices are geodesic curves, asymptotic curves, or lines of the principal curvature. We show that an asymptotic spacelike hyperbolic helix lying on the principal normal surface over the helix and a geodesic spacelike general helix lying on the timelike cylindrical ruled surface, are some examples of non-null relatively normal-slant helices in E-1(3)
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    On null Cartan normal isophotic and normal silhouette curves on a timelike surface in Minkowski 3-space
    (Wiley, 2024) Djordjevic, Jelena; Nesovic, Emilija; Ozturk, Ufuk; Ozturk, Esra B. Koc
    We introduce generalized Darboux frames along a null Cartan curve lying on a timelike surface in Minkowski space E-1(3) and define null Cartan normal isophotic and normal silhouette curves in terms of the vector field that lies in the normal plane of the curve and belongs to its generalized Darboux frame of the first kind. We investigate null Cartan normal isophotic and normal silhouette curves with constant geodesic curvature kg and constant geodesic torsion tau(g). We obtain the parameter equations of their axes and prove that such curves are the null Cartan helices or the null Cartan cubics. In particular, we show that null Cartan normal isophotic curves with a non-zero constant curvatures k(g) and tau(g) have a remarkable property that they are general helices, relatively normal-slant helices and isophotic curves with respect to the same axis. We prove that null Cartan cubics lying on a timelike surface are normal isophotic curves with a spacelike axis and normal silhouette curves with a lightlike axis. We obtain the relation between Minkowski Pythagorean hodograph cubic curves and null Cartan normal isophotic and normal silhouette curves. Finally, we give numerical examples of null Cartan normal isophotic and normal silhouette curves obtained by integrating the system of two the first order differential equations under the initial conditions.
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    Some characterizations of pseudo null isophotic curves in Minkowski 3-space
    (Springer Basel Ag, 2021) Nesovic, Emilija; Öztürk, Ufuk; Öztürk, Esra Betül Koç
    In this paper, we define and characterize pseudo null isophotic curves lying on a non-degenerate surface in Minkowski 3-space. We find the relation between Darboux frame's Darboux vector (angular velocity vector, centrode) (D) over bar of such curves and Frenet frame's Darboux vector D. We prove that D spans their axes if and only if it coincides with (D) over bar. In particular, we show that the only pseudo null isophotic curves whose axes are spanned by D are pseudo null helices. Finally, we provide the related examples.