# Anti-holonomic jets and the Lie bracket

Archivum Mathematicum (1998)

- Volume: 034, Issue: 2, page 311-319
- ISSN: 0044-8753

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topKrupka, Michal. "Anti-holonomic jets and the Lie bracket." Archivum Mathematicum 034.2 (1998): 311-319. <http://eudml.org/doc/248202>.

@article{Krupka1998,

abstract = {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.},

author = {Krupka, Michal},

journal = {Archivum Mathematicum},

keywords = {jet; semi-holonomic jet; anti-holonomic jet; velocity; lie bracket; natural differential operator; jet; semi-holonomic jet; anti-holonomic jet; velocity; Lie bracket; natural differential operator},

language = {eng},

number = {2},

pages = {311-319},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Anti-holonomic jets and the Lie bracket},

url = {http://eudml.org/doc/248202},

volume = {034},

year = {1998},

}

TY - JOUR

AU - Krupka, Michal

TI - Anti-holonomic jets and the Lie bracket

JO - Archivum Mathematicum

PY - 1998

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 034

IS - 2

SP - 311

EP - 319

AB - 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.

LA - eng

KW - jet; semi-holonomic jet; anti-holonomic jet; velocity; lie bracket; natural differential operator; jet; semi-holonomic jet; anti-holonomic jet; velocity; Lie bracket; natural differential operator

UR - http://eudml.org/doc/248202

ER -

## References

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- 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). (193) MR1108622
- Krupka D., Mikolášová V., On the uniqueness of some differential invariants: $d$, $[,]$, $\nabla $, Czechoslovak Math. J. 34 (109) 1984, 588–597. (1984) Zbl0571.53009MR0764440
- Krupka M., First order natural operators on $G$-structures, Preprint No. GA 3/97, Dept. of Math. and Comp. Sc., Silesian Univ. Opava, 1997. (1997) MR1255550
- Krupka M., Natural operators on vector fields and vector distributions, doctoral dissertation, Masaryk University, Brno, 1995. (1995)
- 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). (1992) MR1255550
- Pradines J., Representation des jets non holonomes par des morphisms vectoriels doubles soudés, CRAS Paris, series A 278, 1523–1526 (1974). (1974) MR0388432
- Saunders D., The Geometry of Jet Bundles, Cambridge Univ. Press, 1989. (1989) Zbl0665.58002MR0989588

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