Null-curves in R^{2,n} as flat dynamical systems

TL;DR

This paper demonstrates that the differential equation governing null-curves in pseudo-Euclidean space R^{2,n} forms a flat dynamical system, linking geometric properties with control theory and gauge theories.

Contribution

It establishes the flatness of the null-curve differential equation in pseudo-Euclidean space and explores its relation to gauge theories.

Findings

Null-curves differential equation is a flat dynamical system.

Connection between geometric null-curves and control theory.

Brief discussion on relation to gauge theories.

Abstract

We prove that the differential equation for the null-curves of pseudo-Euclidean space R^{2,n} defines a flat dynamical system in the sense of optimal control theory. The connection with general gauge theories is briefly discussed.