Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces

José del Amor, Ángel Giménez and Pascual Lucas

Advances in Mathematical Physics, 2016, vol. 2016, 1-15

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 infinitely many local symmetries for the null localized induction equation is provided.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5725234

DOI: 10.1155/2016/5725234

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