A Lie algebra structure on variation vector fields along curves in -dimensional space forms
arXiv:1404.0524 · doi:10.1016/j.geomphys.2014.11.010
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.
14 pages