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Title: On the Weilian prolongations of natural bundles (English)
Author: Kolář, Ivan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 62
Issue: 2
Year: 2012
Pages: 487-494
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: Weil algebra
Keyword: Weil functor
Keyword: natural bundle
Keyword: gauge natural bundle
MSC: 58A20
MSC: 58A32
idZBL: Zbl 1265.58001
idMR: MR2990188
DOI: 10.1007/s10587-012-0023-8
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Date available: 2012-06-08T09:47:21Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/142840
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Reference: [1] Kolář, I.: Weil Bundles as Generalized Jet Spaces.Handbook of Global Analysis, Elsevier, Amsterdam (2008), 625-664. Zbl 1236.58010, MR 2389643
Reference: [2] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Berlin: Springer Verlag (1993). MR 1202431
Reference: [3] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors.Differ. Geom. Appl. 11 (1999), 105-115. MR 1712139, 10.1016/S0926-2245(99)00022-4
Reference: [4] Nijenhuis, A.: Natural bundles and their general properties. Geometric objects revisited.Diff. Geometry, in Honor of Kentaro Yano (1972), 317-334. Zbl 0246.53018, MR 0380862
Reference: [5] Weil, A.: Théorie des points proches sur les variétés différentiables.Colloques internat. Centre nat. Rech. Sci. 52 (1953), 111-117 French. Zbl 0053.24903, MR 0061455
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