Ali Uçum

On Generalized Timelike Mannheim Curves 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

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 helix with timelike principal normal and constant timelike slope axis. Moreover, we obtain the parametric equations of spacelike helix with spacelike principal normal, timelike helix and null Cartan helix with timelike slope axis. We also give some related examples and their figures.

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

Abstract In this paper we give the necessary and sufficient conditions for bi-null curves in ℝ63 to be osculating, normal or rectifying curves in terms of their curvature functions.

Lorentzian stationary surfaces and bi-null curves in ℝ25

In this paper, we study Lorentzian stationary surfaces related to bi-null curves in ℝ25. Considering a Gauss-like map, we get Lorentzian stationary surfaces and marginally trapped surfaces in the pseudo-sphere S24(1).

Elastic Sturmian spirals in the Lorentz-Minkowski plane

Abstract 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 details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.

ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE

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 with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.