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On special types of semiholonomic \(3\)-jets. (English) Zbl 1274.58001

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.

MSC:

58A20 Jets in global analysis
58A32 Natural bundles
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References:

[1] C. Ehresmann: 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. (In French.) · Zbl 0561.01027
[2] I. Kolář: The contact of spaces with connection. J. Differ. Geom. 7 (1972), 563–570. · Zbl 0273.53025
[3] I. Kolář: Bundle functors of the jet type. Differential Geometry and Applications. Proceedings of the 7th international conference. Masaryk University, Brno, 1999, pp.231–237.
[4] I. Kolář: A general point of view to nonholonomic jet bundles. Cah. Topol. Géom. Différ. Catég. 44 (2003), 149–160.
[5] I. Kolář: Weil Bundles as Generalized Jet Spaces. Handbook of global analysis, Amsterdam: Elsevier, 2008, pp. 625–665.
[6] I. Kolář: On special types of nonholonomic contact elements. Differ. Geom. Appl. 29 (2011), 135–140. · Zbl 1229.58005
[7] I. Kolář, W.M. Mikulski: On the fiber product preserving bundle functors. Differ. Geom. Appl. 11 (1999), 105–115. · Zbl 0935.58001
[8] I. Kolář, P.W. Michor, J. Slovák: Natural Operations in Differential Geometry. Springer, Berlin, 1993.
[9] P. Libermann: Introduction to the theory of semi-holonomic jets. Arch. Math., Brno 33 (1997), 173–189. · Zbl 0915.58004
[10] G. Vosmanská: Natural transformations of semi-holonomic 3-jets. Arch. Math., Brno 31 (1995), 313–318. · Zbl 0852.58003
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