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Weil algebra; Weil functor; natural bundle; gauge natural bundle
We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration $F(EM)$ of two natural bundles $E$ and $F$. Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.
[1] Kolář, I.: Weil Bundles as Generalized Jet Spaces. Handbook of Global Analysis, Elsevier, Amsterdam (2008), 625-664. MR 2389643 | Zbl 1236.58010
[2] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Berlin: Springer Verlag (1993). MR 1202431
[3] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors. Differ. Geom. Appl. 11 (1999), 105-115. DOI 10.1016/S0926-2245(99)00022-4 | MR 1712139
[4] Nijenhuis, A.: Natural bundles and their general properties. Geometric objects revisited. Diff. Geometry, in Honor of Kentaro Yano (1972), 317-334. MR 0380862 | Zbl 0246.53018
[5] Weil, A.: Théorie des points proches sur les variétés différentiables. Colloques internat. Centre nat. Rech. Sci. 52 (1953), 111-117 French. MR 0061455 | Zbl 0053.24903
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