Null Frenet-Serret Dynamics

TL;DR

This paper develops a Lagrangian framework for the dynamics of null curves in Minkowski space using Frenet-Serret geometry, providing new insights into their deformation and geometric properties.

Contribution

It introduces a deformation theory for null curves based on Frenet-Serret frames and formulates a Lagrangian description of their dynamics in Minkowski space.

Findings

Deformation theory for null curves developed

Lagrangian description of null curve dynamics established

Application to geometric models of null curves

Abstract

We consider the Frenet-Serret geometry of null curves in a three and a four-dimensional Minkowski background. We develop a theory of deformations adapted to the Frenet-Serret frame. We exploit it to provide a Lagrangian description of the dynamics of geometric models for null curves.