Geodesic
The Frölicher-Nijenhuis bracket on some functional spaces
Annales Polonici Mathematici, Tome 68 (1998) no. 2, pp. 97-106 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $C^{∞}(E₁ₓ,E₂ₓ)$, 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.
DOI : 10.4064/ap-68-2-97-106
Keywords: bundle of smooth maps, connection on a functional bundle, Frölicher-Nijenhuis bracket

Ivan Kolář 1 ; Marco Modungo 1

1 
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Ivan Kolář; Marco Modungo. The Frölicher-Nijenhuis bracket on some functional spaces. Annales Polonici Mathematici, Tome 68 (1998) no. 2, pp. 97-106. doi: 10.4064/ap-68-2-97-106

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