A Lie algebra structure on variation vector fields along curves in $2$-dimensional space forms
Differential Geometry
2015-06-19 v1
Abstract
A Lie algebra structure on variation vector fields along an immersed curve in a -dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure for plane curve motions. The Hamiltonian form and the integrability of the planar filament equation is finally discussed from this point of view.
Cite
@article{arxiv.1404.0524,
title = {A Lie algebra structure on variation vector fields along curves in $2$-dimensional space forms},
author = {José del Amor and Ángel Giménez and Pascual Lucas},
journal= {arXiv preprint arXiv:1404.0524},
year = {2015}
}
Comments
14 pages