DSpace Arşivi :: by Yazar "Uçum, Ali" değerine göre listeleniyor

Yazar "Uçum, Ali" seçeneğine göre listele

Listeleniyor 1 - 16 / 16

5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğriler
(Kırıkkale Üniversitesi, 2020) Uçum, Ali; İlarslan, Kazım
Bu tez yedi bölümden oluşmaktadır. Birinci bölüm, giriş kısmına ayrılmıştır. İkinci bölümde tezde gerekli olan kavramlar ve tanımlar verilmiştir. Üçüncü bölümde, 5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğrilerin Frenet çatısı ve denklemleri elde edilmiştir. Ayrıca sabit eğrilikli bi-null eğriler sınıflandırılmış ve parametrik denklemleri elde edilmiştir. Dördüncü bölümde, 5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğrilerin oskülatör, normal ve rektifiyan eğri olması için gerek ve yeter şartlar elde edilmiştir. Beşinci bölümde, 5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğrilerin k-tip bi-null slant helis olması için gerek ve yeter şartlar elde edilmiştir. Altıncı bölümde, 5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğriler ile elde edilen regle yüzeyler çalışılmıştır. Yedinci bölümde, 5-boyutlu 2-indeksli yarı-Öklidyen uzayda bi-null eğriler ile elde edilen stationary yüzeyler incelenmiştir.
A new approach to Mannheim curve in Euclidean 3-space
(Tamkang Univ, 2023) Uçum, Ali; Camcı, Çetin; İlarslan, Kazım
In this article, a new approach is given for Mannheim curves in 3 -dimensional Euclidean space. Thanks to this approach, the necessary and suffi-cient conditions including the known results have been obtained for a curve to be Mannheim curve in E3. In addition, related examples and graphs are given by show-ing that Salkowski and anti-Salkowski curves can be the examples of Mannheim curves and their mates. Finally, the Mannheim partner curves are characterized in E3.
A New Class of Bertrand Curves in Euclidean 4-Space
(Mdpi, 2022) Li, Yanlin; Uçum, Ali; İlarslan, Kazım; Camcı, Çetin
Bertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of (1, 3)-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be (1, 3)-V Bertrand curves. Some related examples are given.
Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame
(Int Electronic Journal Geometry, 2021) Uçum, Ali
In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space H-2 in E-1(3). The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, (X, Y)-Weingarten surface and linear Weingarten surface.
Canal surfaces whose center curve is the curve in the ligthlike cone q2
(Asia Pacific Academic, 2021) Uçum, Ali
In this paper, we obtain the parametrization of the canal surfaces whose center curves are the curves on the lightlike cone Q2 in E31. The parametrization of the canal surface is expressed according to the asymptotic orthonormal frame given in [9]. Then the parallel surface of this surface is studied. Also we define the notion of the associated canal surface. Lastly we give the geometric properties of these surfaces such that Weingarten surface and linear Weingarten surface. © 2021 Asia Pacific Journal of Mathematics.
Generalized Bertrand Curves with Spacelike (1,3)(1,3)-Normal Plane in Minkowski Space-Time
(2016) Uçum, Ali; Keçilioğlu, Osman; İlarslan, Kazım
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.
Inextensible flows of partially null and pseudo null curves in semi-euclidean 4-space with index 2
(Institute of Mathematics, 2016) Uçum, Ali; Erdem, Hatice Altın; İlarslan, Kazım
In this paper, we consider the inextensible ows in semi- Euclidean 4-space with index 2 (E42). We give the necessary and sufficient conditions for the ow to be inextensible and we find the evolution equa- tions for the inextensible ows in semi-Euclidean 4-space with index 2 (E42). © 2016, Institute of Mathematics. All rights reserved.
K-type hyperbolic slant helices in H3
(University of Nis, 2020) Uçum, Ali; İlarslan, Kazım
In the present paper, we give the notion of k-type hyperbolic slant helices in H3, where k 2 {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. © 2020, University of Nis. All rights reserved.
Minkowski uzay-zamanda genelleştirilmiş Bertrand eğrileri
(Kırıkkale Üniversitesi, 2015) Uçum, Ali; İlarslan, Kazım
Bu tez dört bölümden oluşmaktadır. Birinci bölüm, giriş kısmına ayrılmıştır. İkinci bölümde tezde gerekli olan kavramlar ve tanımlar verilmiştir. Üçüncü bölümde, Minkowski uzay-zamanda Bertrand eğrilerinin olmadığına dair teoremler verilmiştir. Dördüncü bölümde, Minkowski uzay-zamanda (1,3)-Bertrand eğrileri, (1,3)-normal düzlemin causal karakterine göre sınıflandırılarak iki alt bölümde verilmiştir. Bu bölümlerde (1,3)-normal düzlemin spacelike veya timelike olma durumlarına göre elde edilen eğrilerin (1,3)-Bertrand eğrileri olmalarını ve (1,3)-Bertrand eşlenik eğrilerinin casual karakterini de ifade eden teoremler elde edilmiştir. Ayrıca ilgili örnekler verilmiştir.
New results concerning Cartan null and pseudo null curves in Minkowski 3-space
(Springer Basel Ag, 2023) Camcı, Çetin; Uçum, Ali; İlarslan, Kazım
In this study, we focus on Cartan null and pseudo null curves in Minkowski 3-space E-1(3). Firstly we define Cartan null and pseudo null equivalent curves and give the related examples. Then we give a construction method for Cartan null curves and it is shown that every Cartan null curve can be obtained from a timelike curve lying in the Lorentz plane in E-1(3). Also a construction method is given for pseudo null curves and we show that all pseudo null curves lie in a lightlike plane in E-1(3). Finally we define a new surface in E-1(3) called surface of pseudo null curves and we obtain the geometric properties of such surfaces.
New type of timelike (1, 3)-Bertrand curves in Minkowski space-time
(Institute of Mathematics, 2023) Camcı, Çetin; İlarslan, Kazım; Uçum, Ali
In the present paper, we define the notion of (1, 3)-V Bertrand curves in E41. Then we find the necessary and sufficient conditions for timelike curves in E41 to be (1, 3)-V Bertrand curves. Finally we give some related examples. © 2023, Institute of Mathematics. All rights reserved.
On osculating, normal and rectifying bi-null curves in R52
(Institute of Mathematics, 2018) İlarslan, Kazım; Sakaki, Makoto; Uçum, Ali
In this paper we give the necessary and sufficient conditions for bi-null curves in R5 2 to be osculating, normal or rectifying curves in terms of their curvature functions. © 2018, Institute of Mathematics. All rights reserved.
Sequential natural mates of Frenet curves in Euclidean 3-space
(Springer Basel Ag, 2021) Camcı, Çetin; Chen, Bang-Yen; İlarslan, Kazım; Uçum, Ali
Associated with a Frenet curve alpha in Euclidean 3-space E-3, there exists the notion of natural mate beta of alpha. In this article, we extend the natural mate beta to sequential natural mates {alpha(1), alpha(2), . . . , alpha(n alpha)} with alpha(1) = beta. We call each curve alpha(i), i epsilon {1, 2, . . . , n(alpha)}, the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve a with its sequential natural mates {alpha(1), alpha(2), . . . , alpha n(alpha)}.
Space Curves Related by a Transformation of Combescure
(Taylor & Francis Ltd, 2021) Çamcı, Çetin; Uçum, Ali; İlarslan, Kazim
In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve a with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the conditions for being Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve of the curve beta obtained from the given curve alpha with the help of Combescure transformation were obtained.
Surfaces of Osculating Circles in Euclidean Space
(Springer Singapore Pte Ltd, 2024) Lopez, Rafael; Camcı, Çetin; Uçum, Ali; İlarslan, Kazım
The aim of this paper is to define a new class of surfaces in Euclidean space using the concept of osculating circle. Given a regular curve C, the surface of osculating circles generated by C is the set of all osculating circles at all points of C. It is proved that these surfaces contain a one-parametric family of planar lines of curvature. A classification of surfaces of osculating circles is given in the family of canal surfaces, Weingarten surfaces, surfaces with constant Gauss curvature and surfaces with constant mean curvature.
Twisted Surfaces in Semi-Euclidean 4-Space with Index 2
(Int Electronic Journal Geometry, 2024) Uçum, Ali; İlarslan, Kazım; Camcı, Çetin
In this paper, we consider the twisted surfaces in semi -Euclidean 4 -space with index 2 . We classify the twisted surface with respect to their spine curve which are non -null or null curves. So, we study the geometric properties of these surfaces. Also we obtain the family of some special surfaces such as flat surfaces, marginally trapped surfaces.

Yazar "Uçum, Ali" seçeneğine göre listele

Sayfa Başına Sonuç

Sıralama seçenekleri