A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms

JOURNAL OF GEOMETRY AND PHYSICS

卷:88

Article

del Amor, Jose¹  Gimenez, Angel²  Lucas, Pascual¹ 

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[2] Univ Miguel Hernandez Elche, Ctr Invest Operat, Elche 03202, Alicante, Spain

关键词: Lie algebra;    Integrable Hamiltonian system;    Curve motions;    Planar filament equation;    mKdV equation;   

DOI  :  10.1016/j.geomphys.2014.11.010

来源: Elsevier

【 摘 要 】

A Lie algebra structure on variation vector fields along an immersed curve in a 2-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 are finally discussed from this point of view. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free