The Frölicher-Nijenhuis bracket on some functional spaces

Volume 68 / 1998

Ivan Kolář, Marco Modungo Annales Polonici Mathematici 68 (1998), 97-106 DOI: 10.4064/ap-68-2-97-106


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.


  • Ivan Kolář
  • Marco Modungo

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