On special types of semiholonomic 3 -jets

Ivan Kolář

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 1, page 165-175
  • ISSN: 0011-4642

Abstract

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First we summarize some properties of the nonholonomic r -jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic r -jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic r -jets. Next we describe an algorithm for finding the nonholonomic r -jet categories. Finally we classify all special types of semiholonomic 3 -jets.

How to cite

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Kolář, Ivan. "On special types of semiholonomic $3$-jets." Czechoslovak Mathematical Journal 63.1 (2013): 165-175. <http://eudml.org/doc/252557>.

@article{Kolář2013,
abstract = {First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets.},
author = {Kolář, Ivan},
journal = {Czechoslovak Mathematical Journal},
keywords = {special type of nonholonomic $r$-jet; nonholonomic $r$-jet category; classification of semiholonomic $3$-jet; special type of nonholonomic -jet; nonholonomic -jet category; classification of semiholonomic 3-jet},
language = {eng},
number = {1},
pages = {165-175},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On special types of semiholonomic $3$-jets},
url = {http://eudml.org/doc/252557},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Kolář, Ivan
TI - On special types of semiholonomic $3$-jets
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 165
EP - 175
AB - First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets.
LA - eng
KW - special type of nonholonomic $r$-jet; nonholonomic $r$-jet category; classification of semiholonomic $3$-jet; special type of nonholonomic -jet; nonholonomic -jet category; classification of semiholonomic 3-jet
UR - http://eudml.org/doc/252557
ER -

References

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  1. Ehresmann, C., Oeuvres Complètes et Commentées. Topologie Algébrique et Géométrie Différentielle. Parties I-1 et I-2. Éd. par Andrée Charles Ehresmann, Suppléments 1 et 2 au Vol. XXIV, Cahiers de Topologie et Géométrie Différentielle (1983), French. (1983) 
  2. Kolář, I., 10.4310/jdg/1214431173, J. Differ. Geom. 7 (1972), 563-570. (1972) Zbl0273.53025MR0415660DOI10.4310/jdg/1214431173
  3. Kolář, I., Bundle functors of the jet type, Differential Geometry and Applications. Proceedings of the 7th international conference Masaryk University, Brno (1999), 231-237. (1999) Zbl0951.58003MR1708910
  4. Kolář, I., A general point of view to nonholonomic jet bundles, Cah. Topol. Géom. Différ. Catég. 44 (2003), 149-160. (2003) Zbl1048.58002MR1985835
  5. Kolář, I., Weil Bundles as Generalized Jet Spaces, Handbook of global analysis Amsterdam: Elsevier (2008), 625-665. (2008) Zbl1236.58010MR2389643
  6. Kolář, I., 10.1016/j.difgeo.2011.03.007, Differ. Geom. Appl. 29 (2011), 135-140. (2011) Zbl1229.58005MR2831821DOI10.1016/j.difgeo.2011.03.007
  7. Kolář, I., Mikulski, W. M., 10.1016/S0926-2245(99)00022-4, Differ. Geom. Appl. 11 (1999), 105-115. (1999) MR1712139DOI10.1016/S0926-2245(99)00022-4
  8. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer, Berlin (1993). (1993) MR1202431
  9. Libermann, P., Introduction to the theory of semi-holonomic jets, Arch. Math., Brno 33 (1997), 173-189. (1997) MR1478771
  10. Vosmanská, G., Natural transformations of semi-holonomic 3 -jets, Arch. Math., Brno 31 (1995), 313-318. (1995) Zbl0852.58003MR1390591

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