Lie brackets on affine bundles

Details Lie brackets on affine bundles Lie brackets on affine bundles

2002-03-12

arxiv.org/abs/math/0203112v2

Ann. Global Anal. Geom. 24 (2003), 101-130

Mathematics

Differential Geometry

22 pages, Lamstex. The revised version, to appear in Annals of Global Analysis and Geometry

Scientific paper

Natural analogs of Lie brackets on affine bundles are studied, based on
natural examples from differential geometry and analytical mechanics. In
particular, a close relation to Lie algebroids and, by a sort of duality, to
affine analogs of Poisson structures is established as well as affine versions
of the complete lift of a section and the Cartan exterior calculus.

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