Emilija Nešović

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.

On Bäcklund transformation and vortex filament equation for pseudo null curves in Minkowski 3-space

In this paper, we introduce Backlund transformation of a pseudo null curve in Minkowski 3-space as a transformation mapping a pseudo null helix to another pseudo null helix congruent to the given one. We also give the sufficient conditions for a transformation between two pseudo null curves in the Minkowski 3-space such that these curves have equal constant torsions. By using the Da Rios vortex filament equation, based on localized induction approximation (LIA), we derive the vortex filament equation for a pseudo null curve and prove that the evolution equation for the torsion is the viscous Burger’s equation. As an application, we show that pseudo null curves and their Frenet frames generate solutions of the Da Rios vortex filament equation.

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

In this paper, we define the Bishop frame of a null Cartan curve in Minkowski space-time 𝔼14. We obtain the Bishop’s frame equations of a null Cartan curve which lies in the timelike hyperplane of ...

On T-slant, N-slant and B-slant helices in pseudo-Galilean space G13

In this paper, we introduce T-slant, N-slant and B-slant helices in the pseudo-Galilean space G3 and define an angle between the spacelike and the timelike isotropic vector lying in the pseudo-Euclidean plane x = 0. In particular, we obtain the explicit parameter equations of the T-slant helices and prove that there are no N-slant and B-slant helices in G3. We also prove that there are no Darboux helices in the same space.

On geometric interpretation of pseudo-angle in Minkowski plane

In this paper, we introduce pseudo-perpendicular vectors in Minkowski plane and give geometric interpretations of the oriented pseudo-angles in terms of the hyperbolic arcs of finite hyperbolic lengths.