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Title: Some functorial prolongations of general connections (English)
Author: Kolář, Ivan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 2
Year: 2018
Pages: 111-117
Summary lang: English
Category: math
Summary: We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket. (English)
Keyword: general connection
Keyword: tangent valued form
Keyword: functorial prolongation
Keyword: Weil functor
MSC: 53C05
MSC: 58A20
MSC: 58A32
idZBL: Zbl 06890308
idMR: MR3813738
DOI: 10.5817/AM2018-2-111
Date available: 2018-06-05T13:37:53Z
Last updated: 2020-01-05
Stable URL:
Reference: [1] Cabras, A., Kolář, I.: Prolongation of tangent valued forms to Weil bundles.Arch. Math. (Brno) 31 (1995), 139–145. MR 1357981
Reference: [2] Ehresmann, C.: Oeuvres complètes et commentés.Cahiers Topol. Géom. Diff. XXIV (Suppl. 1 et 2) (1983).
Reference: [3] Kolář, I.: Handbook of Global Weil Bundles as Generalized Jet Spaces, pp. 625–665, Elsevier, Amsterdam, 2008. MR 2389643
Reference: [4] Kolář, I.: On the functorial prolongations of fiber bundles.Miskolc Math. Notes 14 (2013), 423–431. MR 3144079, 10.18514/MMN.2013.903
Reference: [5] Kolář, I.: Covariant Approach to Weil Bundles.Folia, Masaryk University, Brno (2016).
Reference: [6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry.Springer Verlag, 1993.
Reference: [7] Mangiarotti, L., Modugno, M.: Graded Lie algebras and connections on a fibered space.J. Math. Pures Appl. (9) 63 (1984), 111–120.
Reference: [8] Weil, A.: Théorie des points proches sur les variétes différentielles.Colloque de topol. et géom. diff., Strasbourg (1953), 111–117.


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