2-Degenerate Bertrand curves in Minkowski spacetime

Abstract

In this paper we define a new type of 2-degenerate Cartan curves in Minkowski spacetime $R_{1}^{4}$. We prove that this type of curves contain only the polynomial functions as its components whose third derivative vanish completely. No curve with acceleration zero in $R_{1}^{4}$ is a 2-degenerate Cartan curve, therefore we show that the type of curves that we search for must contain polynomials of degree two among its components.