AV-differential geometry: Poisson and Jacobi structures

JOURNAL OF GEOMETRY AND PHYSICS

卷:52

Article

Grabowska, K ; Grabowski, J ; Urbanski, P

关键词: affine spaces;    vector bundles;    Lie algebroids;    Jacobi structures;    Poisson structures;    Hamilton formalism;   

DOI  :  10.1016/j.geomphys.2004.04.004

来源: Elsevier

【 摘 要 】

Based on ideas of W.M. Tulczyjew, a geometric framework for a frame-independent formulation of different problems in analytical mechanics is developed. In this approach affine bundles replace vector bundles of the standard description and functions are replaced by sections of certain affine line bundles called AV-bundles. Categorial constructions for affine and special affine bundles as well as natural analogs of Lie algebroid structures on affine bundles (Lie affgebroids) are investigated. One discovers certain Lie algebroids and Lie affgebroids canonically associated with an AV-bundle which are closely related to affine analogs of Poisson and Jacobi structures. Homology and cohomology of the latter are canonically defined. The developed concepts are applied in solving some problems of frame-independent geometric description of mechanical systems. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free