Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces

被引：1

作者：

del Amor, Jose ^{[1
]}

Gimenez, Angel ^{[2
]}

Lucas, Pascual ^{[1
]}

机构：

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

[2] Univ Miguel Hernandez Elche, Ctr Invest Operat, Ave Univ S-N, Alicante 03202, Spain

来源：

ADVANCES IN MATHEMATICAL PHYSICS | 2016年 / 2016卷

关键词：

LIE-ALGEBRA STRUCTURE; INTEGRABLE SYSTEMS; EQUATIONS; CLASSIFICATION; PARTICLES; GEOMETRY;

D O I：

10.1155/2016/5725234

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We define a Lie bracket on a certain set of local vector fields along a null curve in a 4-dimensional semi-Riemannian space form. This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space. In particular, a geometric recursion operator generating infinitely many local symmetries for the null localized induction equation is provided.

引用

页数：15

共 32 条

[1] [Anonymous], 1993, DIRAC STRUCTURES INT
[2] Integrable systems in three-dimensional Riemannian geometry
Beffa, GM
Sanders, JA
Wang, JP
[J]. JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (02) : 143 - 167
[3] Blaszak M., 2012, Multi-Hamiltonian theory of dynamical systems
[4] A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms
del Amor, Jose
Gimenez, Angel
Lucas, Pascual
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2015, 88 : 94 - 104
[5] Hamiltonian structure for null curve evolution
del Amor, Jose
Gimenez, Angel
Lucas, Pascual
[J]. NONLINEARITY, 2014, 27 (11) : 2627 - 2641
[6] Dickey L.A, 2003, SOLITON EQUATIONS HA, V26, DOI DOI 10.1142/ASMP
[7] ON THE INTEGRABILITY OF A SYSTEM OF COUPLED KDV EQUATIONS
DODD, R
FORDY, A
[J]. PHYSICS LETTERS A, 1982, 89 (04) : 168 - 170
[8] Relativistic particles and the geometry of 4-D null curves
Fernandez, Angel
Gimenez, Angel
Lucas, Pascual
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2007, 57 (10) : 2124 - 2135
[9] Null helices in Lorentzian space forms
Ferrández, A
Giménez, A
Lucas, P
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2001, 16 (30): : 4845 - 4863
[10] Geometrical particle models on 3D null curves
Ferrández, A
Giménez, A
Lucas, P
[J]. PHYSICS LETTERS B, 2002, 543 (3-4) : 311 - 317

← 1 2 3 4 →