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Title: On special types of semiholonomic $3$-jets (English)
Author: Kolář, Ivan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 63
Issue: 1
Year: 2013
Pages: 165-175
Summary lang: English
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Category: math
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Summary: First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets. (English)
Keyword: special type of nonholonomic $r$-jet
Keyword: nonholonomic $r$-jet category
Keyword: classification of semiholonomic $3$-jet
MSC: 58A20
MSC: 58A32
idZBL: Zbl 1274.58001
idMR: MR3035504
DOI: 10.1007/s10587-013-0011-7
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Date available: 2013-03-01T16:12:54Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/143177
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Reference: [1] Ehresmann, C.: Oeuvres Complètes et Commentées. Topologie Algébrique et Géométrie Différentielle. Parties I-1 et I-2. Éd. par Andrée Charles Ehresmann, Suppléments 1 et 2 au Vol. XXIV.Cahiers de Topologie et Géométrie Différentielle (1983), French.
Reference: [2] Kolář, I.: The contact of spaces with connection.J. Differ. Geom. 7 (1972), 563-570. Zbl 0273.53025, MR 0415660
Reference: [3] Kolář, I.: Bundle functors of the jet type.Differential Geometry and Applications. Proceedings of the 7th international conference Masaryk University, Brno (1999), 231-237. Zbl 0951.58003, MR 1708910
Reference: [4] Kolář, I.: A general point of view to nonholonomic jet bundles.Cah. Topol. Géom. Différ. Catég. 44 (2003), 149-160. Zbl 1048.58002, MR 1985835
Reference: [5] Kolář, I.: Weil Bundles as Generalized Jet Spaces.Handbook of global analysis Amsterdam: Elsevier (2008), 625-665. Zbl 1236.58010, MR 2389643
Reference: [6] Kolář, I.: On special types of nonholonomic contact elements.Differ. Geom. Appl. 29 (2011), 135-140. Zbl 1229.58005, MR 2831821, 10.1016/j.difgeo.2011.03.007
Reference: [7] 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: [8] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer, Berlin (1993). MR 1202431
Reference: [9] Libermann, P.: Introduction to the theory of semi-holonomic jets.Arch. Math., Brno 33 (1997), 173-189. MR 1478771
Reference: [10] Vosmanská, G.: Natural transformations of semi-holonomic $3$-jets.Arch. Math., Brno 31 (1995), 313-318. Zbl 0852.58003, MR 1390591
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