Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as , for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated covariant differential and curvature.
@article{bwmeta1.element.bwnjournal-article-apmv68z2p97bwm,
author = {Ivan Kol\'a\v r and Marco Modungo},
title = {The Fr\"olicher-Nijenhuis bracket on some functional spaces},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {97-106},
zbl = {0982.53024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p97bwm}
}
Ivan Kolář; Marco Modungo. The Frölicher-Nijenhuis bracket on some functional spaces. Annales Polonici Mathematici, Tome 69 (1998) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p97bwm/
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