"Fibre integral in regular Lie algebroids"

New Developments in Differential Geometry, Budapest 1996, KLUWER ACADEMIC PUBLISHERS, Dordrecht, 1999, 173-202. Proceedings of the Conference on Differential Geometry, Budapest, Hungary, 27-30 July 1996.
format dvi format ps publications

The idea of the fibre integral in an oriented bundle is adapted to a regular Lie algebroid. It is based on the well-known result expressing the fibre integral of right-invariant differential forms on a principal bundle via some substitution operator. The object of this article is to define the integration operator ň_A over the adjoint bundle of Lie algebras g in a regular Lie algebroid A over a foliated manifold (M, F) with respect to a cross-section e ÎSecLⁿg, n = rank g, and to demonstrate its main properties.