| Title:
|
Anti-holonomic jets and the Lie bracket (English) |
| Author:
|
Krupka, Michal |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
311-319 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved. (English) |
| Keyword:
|
jet |
| Keyword:
|
semi-holonomic jet |
| Keyword:
|
anti-holonomic jet |
| Keyword:
|
velocity |
| Keyword:
|
lie bracket |
| Keyword:
|
natural differential operator |
| MSC:
|
53A55 |
| MSC:
|
58A20 |
| idZBL:
|
Zbl 0915.58005 |
| idMR:
|
MR1645336 |
| . |
| Date available:
|
2009-02-17T10:12:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107656 |
| . |
| Reference:
|
[1] Ehresmann, Ch.: Extension du calcul des jets aux jets non holonomes.C. R. Acad. Sci., Paris 239, 1762–1764 (1954). Zbl 0057.15603, MR 0066734 |
| Reference:
|
[2] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 434 p. (1993). MR 1202431 |
| Reference:
|
[3] Kolář I.: On the torsion of spaces with connection.Czechoslovak Math. J. 21 (96) 1971, 124–136. MR 0293531 |
| Reference:
|
[4] Krupka D., Janyška J.: Lectures on Differential Invariants.Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis, Mathematica, 1, University J. E. Purkyne, Brno. 193 p. (1990). MR 1108622 |
| Reference:
|
[5] Krupka D., Mikolášová V.: On the uniqueness of some differential invariants: $d$, $[,]$, $\nabla $.Czechoslovak Math. J. 34 (109) 1984, 588–597. Zbl 0571.53009, MR 0764440 |
| Reference:
|
[6] Krupka M.: First order natural operators on $G$-structures.Preprint No. GA 3/97, Dept. of Math. and Comp. Sc., Silesian Univ. Opava, 1997. MR 1255550 |
| Reference:
|
[7] Krupka M.: Natural operators on vector fields and vector distributions.doctoral dissertation, Masaryk University, Brno, 1995. |
| Reference:
|
[8] Krupka M.: On the order reduction of differential invariants.Kowalski, O. et al. (eds.), Differential Geometry and its Applications. Proceedings of the 5th international conference, Opava, Czechoslovakia, August 24–28, 1992, Open Education and Sciences, Opava, Silesian Univ. Math. Publ. (Opava). 1, 321–334 (1993). MR 1255550 |
| Reference:
|
[9] Pradines J.: Representation des jets non holonomes par des morphisms vectoriels doubles soudés.CRAS Paris, series A 278, 1523–1526 (1974). MR 0388432 |
| Reference:
|
[10] Saunders D.: The Geometry of Jet Bundles.Cambridge Univ. Press, 1989. Zbl 0665.58002, MR 0989588 |
| . |
