Kazım İlarslan

On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space

We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space. We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache curves. Finally, we give some examples of such curves.

An application of Ritt-Wu’s zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space

AbstractThe 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

On Smarandache Curves Lying in Lightcone in Minkowski 3-Space

\mathbb{E}_1^3

Nabla 1-Forms on n-Dimensional Time Scales

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On Bishop frame of a null Cartan curve in Minkowski space-time

Abstract 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 a* of the timelike curve a as a timelike curve in Minkowski space-time In this statement, the plane spanned by becomes a spacelike plane. Thus the other possible cases such as timelike and null for the plane spanned by is not considered. In this paper, by taking consideration of all possible causal characters of the plane spanned by we give the necessary and sufficient conditions for timelike curves in to be generalized timelike Mannheim curves in terms of their curvature functions. Also, the related examples are given.

ON GENERAL HELICES WITH SPACELIKE SLOPE AXIS IN MINKOWSKI 3-SPACE

Abstract In this paper we define the spacelike and the null lightcone Smarandache curves of a spacelike lightcone curve α according to the lightcone Frenet frame of a α in Minkowski 3-space. We obtain the lightcone curvature and the expressions for the lightcone Frenet frames vectors of a spacelike Smarandache curve of α. We prove that if the null straight line is the lightcone Smarandache curve of α, then α has non-zero constant lightcone curvature. Finally, we give some examples of lightcone Smarandache curves.

Osculating curves in 4-dimensional semi-Euclidean space with index 2

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space E 3 also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

On osculating, normal and rectifying bi-null curves in ℝ63

In this paper, nabla 1 forms for multivariable functions on n dimensional time scale is presented.