Integrable motions of curves in projective geometries

被引：22
|
作者：
Li, Yanyan [1 ,2 ]
Qu, Changzheng [2 ,3 ]
Shu, Shichang [1 ]
机构：
[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
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2010年 / 60卷 / 6-8期
关键词：
Motion of curve; Integrable system; Projective geometry; Kaup-Kupershmidt equation; KdV equation; SPACE-CURVES; PLANE-CURVES; AFFINE GEOMETRIES; MINKOWSKI SPACE; EQUATIONS; SYSTEMS; EVOLUTION; SOLITONS; FLOWS;
D O I：
10.1016/j.geomphys.2010.03.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：972 / 985
页数：14
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