Generalised connections on affine Lie algebroids

被引：5

作者：

Mestdag, T ^{[1
]}

机构：

[1] State Univ Ghent, Dept Math Phys & Astron, B-9000 Ghent, Belgium

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2003年 / 51卷 / 2-3期

关键词：

affine bundle; Lie algebroid; pseudo-SODE; generalised connection;

D O I：

10.1016/S0034-4877(03)80023-X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate a geometric model for a certain class of first-order differential equations on an affine bundle, called pseudo-SODEs. We mention a generalised version of the concept of connection. Further, if the affine bundle is related to a Lie algebroid, we give a definition for torsion and curvature for such a generalised connection. Next, we show how a pseudo-SODE generates a generalised connection and we characterise this construction by means of the vanishing of torsion.

引用

页码：297 / 305

页数：9

共 16 条

[1]

CANTRIJN F, 2002, IN PRESS DIFF GEOM A

[2]

CARINENA JF, 1999, SYMMETRIES QUANTUM M, P67

[3]

CLEMENTEGALLARD.J, 2000, NONLINEAR CONTROL NE

[4]

CRAMPIN M, 1995, QUADERNI CONSIGLIO N, V47

[5] Lie algebroids, holonomy and characteristic classes [J].

Fernandes, RL .

ADVANCES IN MATHEMATICS, 2002, 170 (01) :119-179

[6]

Fernandes RL, 2000, J DIFFER GEOM, V54, P303

[7] ALGEBRAIC CONSTRUCTIONS IN THE CATEGORY OF LIE ALGEBROIDS [J].

HIGGINS, PJ ;

MACKENZIE, K .

JOURNAL OF ALGEBRA, 1990, 129 (01) :194-230

[8]

Libermann P., 1996, ARCH MATH-BRNO, V32, P147

[9]

Mackenzie K., 1987, LONDON MATH SOC LECT, V124

[10] Lie algebroid structures and Lagrangian systems on affine bundles [J].

Martínez, E ;

Mestdag, T ;

Sarlet, W .

JOURNAL OF GEOMETRY AND PHYSICS, 2002, 44 (01) :70-95

← 1 2 →