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Title: On the underlying lower order bundle functors (English)
Author: Doupovec, Miroslav
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 4
Year: 2005
Pages: 901-916
Summary lang: English
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Category: math
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Summary: For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with $m$-dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors. (English)
Keyword: bundle functor
Keyword: Weil bundle
Keyword: natural transformation
MSC: 58A05
MSC: 58A20
MSC: 58A32
idZBL: Zbl 1081.58001
idMR: MR2184371
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Date available: 2009-09-24T11:28:46Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128032
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Reference: [1] M. Doupovec and I.  Kolář: Iteration of fiber product preserving bundle functors.Monatsh. Math. 134 (2001), 39–50. MR 1872045, 10.1007/s006050170010
Reference: [2] I. Kolář: Affine structure on Weil bundles.Nagoya Math.  J. 158 (2000), 99–106. MR 1766571
Reference: [3] I. Kolář: A general point of view to nonholonomic jet bundles.Cahiers Topo. Geom. Diff. Categoriques XLIV (2003), 149–160. MR 1985835
Reference: [4] I. Kolář, P. W. Michor and J. Slovák: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431
Reference: [5] I. Kolář and W. M. Mikulski: On the fiber product preserving bundle functors.Diff. Geom. Appl. 11 (1999), 105–115. MR 1712139, 10.1016/S0926-2245(99)00022-4
Reference: [6] M. Kureš: On the simplicial structure of some Weil bundles.Rend. Circ. Mat. Palermo, Serie  II, Suppl. 63 (2000), 131–140. MR 1758088
Reference: [7] J. E. White: The Method of Iterated Tangents with Applications in Local Riemannian Geometry.Pitman Press, , 1982. Zbl 0478.58002, MR 0693620
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