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Fibre Integral in Regular Lie Algebroids

In: New Developments in Differential Geometry, Budapest 1996

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  • Jan Kubarski

    (Technical University of ódź, Institute of Mathematics)

Abstract

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 f 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 ɛ ∈ Sec ⋀ n g, n = rank g, and to demonstrate its main properties.

Suggested Citation

  • Jan Kubarski, 1999. "Fibre Integral in Regular Lie Algebroids," Springer Books, in: J. Szenthe (ed.), New Developments in Differential Geometry, Budapest 1996, pages 173-202, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5276-1_12
    DOI: 10.1007/978-94-011-5276-1_12
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