Anti-holonomic jets and the Lie bracket

Michal Krupka

Archivum Mathematicum (1998)

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

Abstract

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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.

How to cite

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Krupka, 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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  1. Ehresmann, Ch., Extension du calcul des jets aux jets non holonomes, C. R. Acad. Sci., Paris 239, 1762–1764 (1954). (1954) Zbl0057.15603MR0066734
  2. Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 434 p. (1993). (1993) MR1202431
  3. Kolář I., On the torsion of spaces with connection, Czechoslovak Math. J. 21 (96) 1971, 124–136. (1971) MR0293531
  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). (193) MR1108622
  5. Krupka D., Mikolášová V., On the uniqueness of some differential invariants: d , [ , ] , ∇ , Czechoslovak Math. J. 34 (109) 1984, 588–597. (1984) Zbl0571.53009MR0764440
  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. (1997) MR1255550
  7. Krupka M., Natural operators on vector fields and vector distributions, doctoral dissertation, Masaryk University, Brno, 1995. (1995) 
  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). (1992) MR1255550
  9. Pradines J., Representation des jets non holonomes par des morphisms vectoriels doubles soudés, CRAS Paris, series A 278, 1523–1526 (1974). (1974) MR0388432
  10. Saunders D., The Geometry of Jet Bundles, Cambridge Univ. Press, 1989. (1989) Zbl0665.58002MR0989588

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