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In this paper, we obtain the Frenet equations of a pseudo null and a partially null curves, lying fully in the semi-Euclidean space R 4 2 , and classify all such curves with constant curvatures. (2000): 53C50, 53C40. Mathematics Subject Classification

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In this paper, we introduce Bäcklund 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.

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In this paper, we classify the ruled surfaces with a pseudo null base curve in Minkowski 3-space as spacelike, timelike and lightlike surfaces and obtain the corresponding striction curve and distribution parameter. In particular, we give some examples of lightlike developable surfaces with pseudo null base curve. As an application, we show that pseudo null curve and it's frame vectors generate new solutions of the Da Rios vortex filament equation.

In this paper, we define k‐type null Cartan slant helices lying on a timelike surface in Minkowski space double-struckE13 according to their Darboux frame, where k ∈ {0,1,2}. We study these helices by using their geodesic curvature, normal curvature , and geodesic torsion. Additionally, we determine their axes and consider the special cases when the mentioned helices are geodesic curves and principal curvature lines lying on the timelike surface in double-struckE13. Furthermore, we obtain some interesting relations between 0‐, 1‐, and 2‐type null Cartan slant helices.