| Title:
|
Introduction to the theory of semi-holonomic jets (English) |
| Author:
|
Libermann, Paulette |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
173-189 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
non holonomic jet |
| Keyword:
|
semi-holonomic jet |
| Keyword:
|
differential system |
| Keyword:
|
connection |
| Keyword:
|
G-structure |
| MSC:
|
53C05 |
| MSC:
|
53C10 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0915.58004 |
| idMR:
|
MR1478771 |
| . |
| Date available:
|
2008-06-06T21:33:10Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107609 |
| . |
| Reference:
|
[B] Bernard, D.: Thèse.Ann. Inst. Fourier 10 (1960), 151–270. Zbl 0104.14002, MR 0126800 |
| Reference:
|
[E] Ehresmann, C., 1. Structures infinitèsimales et pseudogroupes de Lie, Colloq. Intern. CNRS, Geom. Diff. Strasbourg (1953), 97–110. 2. Proc. Intern. Congress Amsterdam (1954) II 478. 3. Compte-rendus, Acad. Sc. Paris 239 (1954) 1762; 240 (1955), 397, 1755, 246 (1958), 360. 4. Connexions d’ordre supérieur, Atti 5 Cong. dell Unione Italiana 1955, Roma (1956), 326–328. Oeuvres completes, P. I and II, Amiens 1984: .. MR 0063123 |
| Reference:
|
[CK] Cabras, A., Kolář, I.: Connections on some functional bundles.Czechoslovak Math. J. 45 (120) 1995, Praha, 529–548. MR 1344519 |
| Reference:
|
[J] Janyška, J., 1. Geometric properties of prolongation functors, Časopis pěst. mat. 110 (1985), 77–86. 2. On natural operations with linear connections, Czechoslovak Math. J. 35 (110) (1985), 106–115: .. MR 0791280 |
| Reference:
|
[JK] Janyška, J., Kolář, I.: Connections naturally induced on the second order frame bundle.Arch. Math. (Brno) 22, No 1, (1986), 21–28. MR 0868117 |
| Reference:
|
[K] Kolář, I., 1. Order of holonomy and geometric objects of manifolds with connection, Comm. Math. Universitatis Carolinae 10, 4 (1969). 2. Order of holonomy of a surface with projective connection, Časopis pěst. mat. 96 (1971), 73–80. 3. On the torsion of spaces with connection, Czechoslovak Math. J. 21 (96) (1971), 124–136. 4. Higher order torsions of spaces with Cartan connection, Cahiers Top. Geom. Differentielle 12 (1971), 137–146. 5. The contact of spaces with connection, Journ. of Diff. Geometry, 7, No 3 and 4, (1972), 563–570. 6. On the absolute differentiation of geometric object fields, Ann. Polon. Math. 27 (1973), 293–304. 7. Some operations with connections, Math. Nachr. 69 (1975), 297–306. 8. Reducibility of connections on the prolongations of vector bundles, Colloq. Mathematicum, XXX (1974), 245–257. 9. A generalization of the torsion form, Časopis pěst. mat. 100 (1975), 284–290. 10. Generalized $G$-structures and $G$-structures of higher order, Boll. Union Math. Ital. 12, Suppl. fasc. 3 (1975), 245–256. 11. On generalized connections, Beitrage zur Alg. Geom. 11 (1981), 29–34. 12. Higher order absolute differentiation, Diff. Geom. Banach Center Publ. 12, Warszaw (1984), 153–161. 13. Natural operations with connections on second order frame bundles, Coll. Math. Societais János Bolyai, 46, Topics in Diff. Geom. Debrecen (1984), 715–732. 14. Some natural operators in differential geometry, Diff. Geom. and its applications. Proceed. of the Conf. August 1986, Brno: .. MR 0264539 |
| Reference:
|
[KMS] Kolář, I., Michor, P., Slovák, J.: Natural Operations in Differential Geometry.Springer-Verlag, 1993. MR 1202431 |
| Reference:
|
[KM] Kolář, I., Modugno, M.: Natural maps on the iterated jet prolongation of a fibered manifold.Annali di Matem. pura e appt. (IV), CLVIII (1991), 151–165. MR 1131848 |
| Reference:
|
[KVi] Kolář, I., Virsik, G.: Connections in first principal prolongations.Rendiconti, Palermo. |
| Reference:
|
[KVo] Kolář, I., Vosmanská, G.: Natural operations with second order jets.Rendiconti Circolo Matem. Palermo, II, No 14 (1987), 179–186. MR 0920854 |
| Reference:
|
[Leh] Lehmann, D.: Sur l’ integrabilité des $G$-structures.Symp. Math. X (Convegno Geom. Diff.) Roma (1971), 127–140. Zbl 0252.53030, MR 0362125 |
| Reference:
|
[L] Libermann, P., 1. Geométrie des prolongements des fibrés vectoriels, Coll. Int. CNRS Grenoble (1964), Ann. Inst. Fourier XIV, fasc. 1, 145–172. 2. Connexions d’ordre supérieur et tenseur de structure, Atti Conv. Int. Geom. Diff., Bologna IX, 1967. 3. Prolongements des fibrés principaux et groupoides différentiables, Sémin. Analyse Globale Montréal (1969), 7–108. 4. Presque parallélisme, Diff. Geom. in honour of K. Yano, Tokyo (1972), 243–252. 5. Groupoides différentiables et presque parallélisme, Symp. Math. X (Convegno di Geom. Diff.) Roma (1971), 59–93. 6. Parallélismes, Journ. Diff. Geometry 8 (1973), 511–539. 7. Introduction à l’étude de certains systémes différentiels, Geom. and Diff. Geom., Haifa, Lecture Notes in Math. 792 (1979) and 3$^e$ Colloque sur les catégories Cahiers Top. et Geom. Diff. XXIII - 1 (1982), 55–72. 8. Lie algebroids and Mechanics, Arch. Math. 32 (1996), 147–162. 9. Pseudogroupes infinitésimaux, Bull. Soc. Math. France 87 (1959), 409–425: .. MR 0123279 |
| Reference:
|
[M] Molino, P.: Sur quelques propiétés des $G$-structures.Journ. Diff. Geometry 6 (1972), 489–518. MR 0423441 |
| Reference:
|
[P] Pradines, J., 1. Compte-rendus, Acad. Sci. Paris 278 (1974), série A, 1523–1526, 1557–1560, 1587–1590. 2. Fibrés vectoriels doubles et calcul des jets non holonomes, Esquisses Math. 29, Amiens (1977): .. |
| Reference:
|
[Ve] Ver Eecke, P.: Thése.Cahiers Top. Geom. Diff. V (1963). |
| Reference:
|
[Vi] Virsik, G., 1. On the holonomity of higher order connections, Cahiers Top. Geom. Diff. 12 (1971), 197–212. 2. Total connections in Lie groupoids, Arch. Math. (Brno) 31 (1995), 183–200: .. MR 0305294 |
| Reference:
|
[Vo] Vosmanská, G.: Natural transformations of semi-holonomic 3-jets.Arch. Math. (Brno) 31 (1995), 313–318. MR 1390591 |
| Reference:
|
[Y] Yuen, P.: Prolongements des $G$-structures.Thése Esquisses Math. 11 (1970). |
| . |
