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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 introduce the notion of the second kind twisted surfaces in Minkowski 3-space. We classify all non-degenerate second kind twisted surfaces in terms of flat, minimal, constant Gaussian and constant mean curvature surfaces, with respect to a chosen lightlike transversal bundle. We also prove that a lightlike second kind twisted surfaces, with respect to a chosen lightlike transversal vector bundle, are the lightcones, the lightlike binormal surfaces over pseudo null base curve and the lightlike ruled surfaces with null rulings whose base curve lies on lightcone.