Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
jet bundle; semiholonomic $r$-jet
jet bundle; semiholonomic $r$-jet
Summary:
It is well known that the concept of holonomic $r$-jet can be geometrically characterized in terms of the contact of individual curves. However, this is not true for the semiholonomic $r$-jets, [5], [8]. In the present paper, we discuss systematically the semiholonomic case.
References:
[1] Cabras, A., Kolář, I.: Prolongation of tangent valued forms. Arch. Math. (Brno) 38 (2002), 243–254. MR 1942654
[2] Doupovec, M., Mikulski, W.M.: Holonomic extension of connections and symmetrization of jets. Rep. Math. Phys. 60 (2007), 299–316. DOI 10.1016/S0034-4877(07)80141-8 | MR 2374824 | Zbl 1160.58001
[3] Ehresmann, C.: Extension du calcul des jets aux jets non holonomes. CRAS Paris 239 (1954), 1762–1764. MR 0066734 | Zbl 0057.15603
[4] Ehresmann, C.: Sur les connexions d’ordre supériour. Atti del V. Cong. dell Unione Mat. Italiana, Roma Cremonese (1956), 326–328.
[5] Kolář, I.: The contact of spaces with connection. J. Differential Geometry 7 (1972), 563–570. DOI 10.4310/jdg/1214431173 | MR 0415660 | Zbl 0273.53025
[6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, 1993.
[7] Libermann, P.: Prolongations des fibrés principaux et groupoides différentiables. Sémin. Analyse Globale Montréal, 1969, pp. 7–108. MR 0356117
[8] Libermann, P.: Introduction to the theory of semiholonomic jets. Arch. Math. (Brno) 33 (1997), 173–189. MR 1478771
[9] Libermann, P.: Charles Ehresmann’s concepts in differential geometry. Banach Center Publications 76 (2007), 35–50, Polish Academy of Sciences, Warszawa. DOI 10.4064/bc76-0-2 | MR 2342844
Search
Partner of
