Yazar "Ucum, Ali" için listeleme
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Bi-null curves with constant curvatures in R-2(5)
Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim (Springer Basel Ag, 2019)In the present paper, we classify bi-null curves with constant curvatures in semi-Euclidean 5-space R-2(5) with index 2. -
Elastic Sturmian spirals in the Lorentz-Minkowski plane
Ucum, Ali; Ilarslan, Kazim; Mladenov, Ivailo M. (De Gruyter Poland Sp Zoo, 2016)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 ... -
General Helices with Lightlike Slope Axis
Camci, Cetin; Ilarslan, Kazim; Ucum, Ali (Univ Nis, Fac Sci Math, 2018)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 ... -
General Helices with Timelike Slope Axis in Minkowski 3-Space
Ucum, Ali; Camci, Cetin; Ilarslan, Kazim (Springer Basel Ag, 2016)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 ... -
Generalized Bertrand Curves with Spacelike (1,3)-Normal Plane in Minkowski Space-Time
Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim (Scientific Technical Research Council Turkey-Tubitak, 2016)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 ... -
Generalized Bertrand curves with timelike (1,3)-normal plane in Minkowski space-time
Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim (Academic Publication Council, 2015)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. ... -
Generalized pseudo null Bertrand curves in semi-Euclidean 4-space with index 2
Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim (Springer-Verlag Italia Srl, 2016)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 ... -
k-Type Bi-null Cartan Slant Helices in R-3(6)
Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto (Southeast Asian Mathematical Soc-Seams, 2018)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 bi-null slant helices in R-2(5)
Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto (Springer Basel Ag, 2017)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 ... -
Lorentzian stationary surfaces and bi-null curves in R-2(5)
Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim (World Scientific Publ Co Pte Ltd, 2017)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). -
A new approach to Bertrand curves in Euclidean 3-space
Camci, Cetin; Ucum, Ali; Ilarslan, Kazim (SPRINGER BASEL AG, 2020)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 ... -
New Types of Canal Surfaces in Minkowski 3-Space
Ucum, Ali; Ilarslan, Kazim (Springer Basel Ag, 2016)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 ... -
Note On Bertrand B-Pairs Of Curves In Minkowski 3-Space
Ilarslan, Kazim; Ucum, Ali; Aslan, Nihal Kilic; Nesovic, Emilija (Honam Mathematical Soc, 2018)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 ... -
On (1, 3)-Cartan null Bertrand curves in semi-Euclidean 4-space with index 2
Ucum, Ali; Ilarslan, Kazim; Sakaki, Makoto (Springer Basel Ag, 2016)In this paper, we study generalized Cartan null Bertrand curves in semi-Euclidean 4-space E-2(4) with index 2. -
On bi-null Cartan curves in semi-Euclidean 6-space with index 3
Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim (Springer Basel Ag, 2016)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 ... -
On Generalized Spacelike Mannheim Curves in Minkowski Space-Time
Ilarslan, Kazim; Ucum, Ali; Nesovic, Emilija (Natl Acad Sciences India, 2016)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 ... -
On Generalized Timelike Mannheim Curves in Minkowski Space-time
Ucum, Ali; Nesovic, Emilija; Ilarslan, Kazim (Taylor & Francis Ltd, 2015)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 ... -
On osculating, normal and rectifying bi-null curves in (6)(3)
Ucum, Ali; Sakaki, Makoto; Ilarslan, Kazim (Taylor & Francis Ltd, 2017)In this paper we give the necessary and sufficient conditions for bi-null curves in (6)(3) to be osculating, normal or rectifying curves in terms of their curvature functions. -
On Timelike Bertrand Curves In Minkowski 3-Space
Ucum, Ali; Ilarslan, Kazim (Honam Mathematical Soc, 2016)In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve ... -
Ruled surfaces with bi-null curves in R-2(5)
Sakaki, Makoto; Ucum, Ali; Ilarslan, Kazim (Springer-Verlag Italia Srl, 2017)In the present paper, we discuss the geometric properties of two classes of ruled surfaces whose directrix curve is a bi-null curve in semi-Euclidean space R-2(5). We get some classes of flat marginally trapped surfaces in R-2(5).