2-Degenerate Bertrand curves in Minkowski spacetime

TL;DR

This paper introduces a new class of 2-degenerate Cartan curves in Minkowski spacetime, characterized by polynomial components with vanishing third derivatives, and explores their properties and constraints.

Contribution

It defines 2-degenerate Cartan curves in Minkowski space and characterizes their polynomial component structure, expanding the understanding of degenerate curves in this setting.

Findings

Curves contain only polynomial functions with third derivatives equal to zero.

No curve with zero acceleration in R_{1}^{4} is a 2-degenerate Cartan curve.

Such curves must include quadratic polynomial components.

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.