Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces

Abstract EN

We define a Lie bracket on a certain set of local vector fields along a null curve in a 4-dimensional semi-Riemannian space form.

This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space.

In particular, a geometric recursion operator generating infinitely many local symmetries for the null localized induction equation is provided.