Yazar "Nesovic, Emilija" seçeneğine göre listele
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Öğe The first kind and the second kind osculating curves in Minkowski space-time(Publ House Bulgarian Acad Sci, 2009) İlarslan, Kazim; Nesovic, EmilijaIn this paper we define the first kind and the second kind osculating curve in Minkowski space-time E-1(4). We restrict our investigation of osculating curves in E-1(4) to spacelike curves whose Frenet frame contains only non-null vector fields, as well as to timelike curves and characterize such curves in terms of their curvature functions. Moreover, we obtain the explicit equations of such osculating curves with constant curvatures.Öğe Mannheim B-Curve Couples In Minkowski 3-Space(TAMKANG UNIV, 2020) Ilarslan, Kazim; Ucum, Ail; Nesovic, Emilija; Aslan, Nihail KilicIn this paper, we define null Cartan Mannheim and pseudo null Mannheim curves in Minkowski 3-space according to their Bishop frames. We obtain the necessary and the sufficient conditions for pseudo null curves to be Mannheim B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Mannheim B-curves, by considering the cases when their Mannheim B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Mannheim B-curve pairs.Öğe Note On Bertrand B-Pairs Of Curves In Minkowski 3-Space(Honam Mathematical Soc, 2018) Ilarslan, Kazim; Ucum, Ali; Aslan, Nihal Kilic; Nesovic, EmilijaIn 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.Öğe A Note On Lamarle Formula Inminkowski 3-Space(Tamkang Univ, 2018) Ozturk, Ufuk; Ilarslan, Kazim; Ozturk, Esra Betul Koc; Nesovic, EmilijaThe Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field inMinkowski 3-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples.Öğe On Bishop frame of a null Cartan curve in Minkowski space-time(World Scientific Publ Co Pte Ltd, 2018) Ilarslan, Kazim; Nesovic, EmilijaIn this paper, we define the Bishop frame of a null Cartan curve in Minkowski space-time E-1(4). We obtain the Bishop's frame equations of a null Cartan curve which lies in the timelike hyperplane of E-1(4). We show that a null Cartan cubic lying in the timelike hyperplane of E-1(4) has two Bishop frames, one of which coincides with its Cartan frame. We also derive the Bishop's frame equation of the null Cartan curve which has the third Cartan curvature K-3(s) not equal 0. As an application, we find a solution of the null Betchov-Da Rios vortex filament equation in terms of a null Cartan curve and its Bishop frame, which generates a timelike Hasimoto surface.Öğe On Generalized Null Mannheim Curves In Minkowski Space-Time(Publications L Institut Mathematique Matematicki, 2016) Grbovic, Milica; Ilarslan, Kazim; Nesovic, EmilijaWe define generalized null Mannheim curves in Minkowski space-time and characterize them and their generalized Mannheim mate curves in terms of curvature functions, and obtain relations between their frames. We provide examples of such curves.Öğe On Generalized Spacelike Mannheim Curves in Minkowski Space-Time(Natl Acad Sciences India, 2016) Ilarslan, Kazim; Ucum, Ali; Nesovic, EmilijaIn 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.Öğe On Generalized Timelike Mannheim Curves in Minkowski Space-time(Taylor & Francis Ltd, 2015) Ucum, Ali; Nesovic, Emilija; Ilarslan, KazimIn 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.Öğe On Pseudospherical Smarandache Curves in Minkowski 3-Space(Hindawi Ltd, 2014) Öztürk, Esra Betül Koç; Öztürk, Ufuk; İlarslan, Kazım; Nesovic, EmilijaIn this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame's vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curve alpha, then alpha has constant geodesic curvature. Finally, we give some examples of pseudospherical Smarandache curves.Öğe On Ruled Surfaces with Pseudo Null Base Curve in Minkowski 3-Space(Int Electronic Journal Geometry, 2016) Nesovic, Emilija; Ozturk, Ufuk; Ozturk, Esra B. Koc; Ilarslan, KazimIn this paper, we classify the ruled surfaces with a pseudo null base curve in Minkowski 3-space as spacelike, timelike and lightlike surfaces and obtain the corresponding striction curve and distribution parameter. In particular, we give some examples of lightlike developable surfaces with pseudo null base curve. As an application, we show that pseudo null curve and it's frame vectors generate new solutions of the Da Rios vortex filament equation.Öğe ON SMARANDACHE CURVES LYING IN LIGHTCONE IN MINKOWSKI 3-SPACE(Taylor & Francis Ltd, 2014) Ozturk, Ufuk; Ozturk, Esra Betul Koc; Ilarslan, Kazim; Nesovic, EmilijaIn this paper we define the spacelike and the null lightcone Smarandache curves of a spacelike lightcone curve a according to the lightcone Frenet frame of a a in Minkowski 3-space. We obtain the lightcone curvature and the expressions for the lightcone Frenet frame's vectors of a spacelike Smarandache curve of a. We prove that if the null straight line is the lightcone Smarandache curve of a, then a has non-zero constant lightcone curvature. Finally, we give some examples of lightcone Smarandache curves.Öğe Some characterizations of null osculating curves in the Minkowski space-time(Estonian Academy Publishers, 2012) Ilarslan, Kazim; Nesovic, EmilijaIn this paper we give the necessary and sufficient conditions for null curves in E-1(4), to be osculating curves in terms of their curvature functions. In particular, we obtain some relations between null normal curves and null osculating curves as well as between null rectifying curves and null osculating curves. Finally, we give some examples of the null osculating curves in E-1(4).Öğe SOME CHARACTERIZATIONS OF PSEUDO AND PARTIALLY NULL OSCULATING CURVES IN MINKOWSKI SPACE-TIME(Int Electronic Journal Geometry, 2011) Ilarslan, Kazim; Nesovic, EmilijaIn this paper, we characterize pseudo and partially null osculating curves of the first and second kind in Minkowski space-time E-1(4) in terms of their curvature functions. We give the necessary and sufficient conditions for pseudo and partially null curves to be osculating curves. In particular, we show that there exists a simple relationship between pseudo and partially null osculating curves and pseudo and partially null normal and rectifying curves. Finally, we obtain some explicit parameter equations of pseudo and partially null osculating curves in E-1(4).Öğe SOME CHARECTERIZATIONS OF OSCULATI NG CURVES IN THE EUCLIDEAN SPACES(De Gruyter Poland Sp Zoo, 2008) Ilarslan, Kazim; Nesovic, EmilijaIn this paper, we give some characterization for a osculating curve in 3-dimensional Euclidean space and we define a osculating curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement B-1(perpendicular to) of its first binormal vector field B-1. In particular, we study the osculating curves in E-4 and characterize such curves in terms of their curvature functionsÖğe SOME RELATIONS BETWEEN NORMAL AND RECTIFYING CURVES IN MINKOWSKI SPACE-TIME(Int Electronic Journal Geometry, 2014) Ilarslan, Kazim; Nesovic, EmilijaIn this paper, we firstly give the necessary and sufficient conditions for null, pseudo null and partially null curves in Minkowski space-time to be normal curves. We prove that the null, pseudo null and partially null normal curves have a common property that their orthogonal projection onto non-degenerate hyperplane of E(1)(4 )or onto lightlike 2-plane of E(1)(4 )is the corresponding rectifying curve. Finally, we give some examples of such curves in E-1(4).Öğe Tensor product surfaces of a Lorentzian space curve and a Euclidean plane curve(Academic Publication Council, 2007) İlarslan, Kazım; Nesovic, EmilijaIn this paper, we classify all minimal, totally real and complex tensor product surfaces of a Lorentzian space curve and a Euclidean plane curve.
