Integrable motions of curves in projective geometries

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Li, Yanyan^1,2  Qu, Changzheng^2,3  Shu, Shichang¹ 

[1] Xianyang Normal Univ, Inst Math & Informat Sci, Xianyang 712000, Peoples R China

[2] NW Univ Xian, Ctr Nonlinear Studies, Xian 710069, Peoples R China

[3] NW Univ Xian, Dept Math, Xian 710069, Peoples R China

关键词: Motion of curve;    Integrable system;    Projective geometry;    Kaup-Kupershmidt equation;    KdV equation;   

DOI  :  10.1016/j.geomphys.2010.03.001

来源: Elsevier

【 摘 要 】

In this paper, integrable systems satisfied by the curvatures of curves under inextensible motions in projective geometries are identified. It is shown that motions of curves in two-, three- and four-dimensional projective geometries are respectively related to the Kaup-Kupershmidt hierarchy, a coupled Kaup-Kupershmidt-KdV system and their extension. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.

【 授权许可】

Free