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Title: On the geometry of vertical Weil bundles (English)
Author: Kolář, Ivan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 50
Issue: 5
Year: 2014
Pages: 317-322
Summary lang: English
Category: math
Summary: We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections. (English)
Keyword: Weil bundle
Keyword: fiber product preserving bundle functor
Keyword: flow natural map
Keyword: weak principal connection
MSC: 53C05
MSC: 58A20
MSC: 58A32
idZBL: Zbl 06487015
idMR: MR3303780
DOI: 10.5817/AM2014-5-317
Date available: 2015-01-07T14:59:25Z
Last updated: 2016-04-02
Stable URL:
Reference: [1] Cabras, A., Kolář, I.: Prolongation of second order connections to vertical Weil bundles.Arch. Math. (Brno) 37 (2001), 333–347. Zbl 1090.58003, MR 1879456
Reference: [2] Cabras, A., Kolář, I.: On the functorial prolongations of principal bundles.Comment. Math. Univ. Carol. 47 (2006), 719–731. Zbl 1150.58002, MR 2337425
Reference: [3] Čap, A., Slovák, J.: Parabolic Geometries I.Mathematical Surveys and Monographs, vol. 154, AMS, Providence, USA, 2009. Zbl 1183.53002, MR 2532439, 10.1090/surv/154/03
Reference: [4] Kolář, I.: On the geometry of fiber product preserving bundle functors.Differential Geometry and its Applications, Proceedings, Silesian University of Opava, 2002, pp. 63–72. MR 1978765
Reference: [5] Kolář, I.: Handbook of Global Weil Bundles as Generalized Jet Spaces, pp. 625–664, Elsevier, Amsterdam, 2008. MR 2389643
Reference: [6] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Verlag, 1993. MR 1202431
Reference: [7] Kolář, I., Mikulski, W.M.: On the fiber product preserving bundle functors.Differential Geom. Appl. 11 (1999), 105–115. MR 1712139, 10.1016/S0926-2245(99)00022-4
Reference: [8] Mikulski, W.M.: Fiber product preserving bundle functors as modified vertical Weil functors.11pp., to appear in Czechoslovak Math. J.
Reference: [9] Weil, A.: Théorie des points proches sur les variétes différentielles.Colloque de topol. et géom. diff., Strasbourg , 1953, pp. 111–117. MR 0061455


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