Null curve evolution in four-dimensional pseudo-Euclidean spaces
Mathematical Physics
2016-04-11 v2 math.MP
Abstract
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 infinite many local symmetries for the null localized induction equation is provided.
Keywords
Cite
@article{arxiv.1603.02820,
title = {Null curve evolution in four-dimensional pseudo-Euclidean spaces},
author = {José del Amor and Ángel Giménez and Pascual Lucas},
journal= {arXiv preprint arXiv:1603.02820},
year = {2016}
}