Geometrical Particle Models on 3d Lightlike Curves

Abstract

The (2+1)-dimensional mechanical systems associated with lightlike curves are considered. We studied the action whose Lagrangian depends quadratically on the Cartan curvature (torsion). Some conservation laws are given and the motion equation for a special case is completely solved by using geometrical methods.

Slant helices: a new approximation

“…Finally, in the case of null curves, and in a similar way as before, we will say that the vector field V (s) is a Killing vector field along γ if the following conditions are satisfied [5,6]:…”

On dual r-elastic line

“…More recently Langer and Singer studied the closed elastic curves in the 2-sphere and in the hyperbolic plane [9]. Huang and Liao studied geometrical particle models on 3D lightlike curves [7]. In [1], authors studied Wilmore-Chen variational problem in pseudo-Riemannian spaces.…”