Higher order Cartan connections

Juraj Virsik

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 4, page 343-354
  • ISSN: 0044-8753

Abstract

top
A Cartan connection associated with a pair P ( M , G ' ) P ( M , G ) is defined in the usual manner except that only the injectivity of ω : T ( P ' ) T ( G ) e is required. For an r -th order connection associated with a bundle morphism Φ : P ' P the concept of Cartan order q r is defined, which for q = r = 1 , Φ : P ' P , and dim M = dim G / G ' coincides with the classical definition. Results are obtained concerning the Cartan order of r -th order connections that are the product of r first order (Cartan) connections.

How to cite

top

Virsik, Juraj. "Higher order Cartan connections." Archivum Mathematicum 032.4 (1996): 343-354. <http://eudml.org/doc/18475>.

@article{Virsik1996,
abstract = {A Cartan connection associated with a pair $P(M,G^\{\prime \})\subset P(M,G)$ is defined in the usual manner except that only the injectivity of $\omega :T(P^\{\prime \})\rightarrow T(G)_\{e\}$ is required. For an $r$-th order connection associated with a bundle morphism $\Phi :P^\{\prime \}\rightarrow P$ the concept of Cartan order $q\le r$ is defined, which for $q=r=1, \Phi :P^\{\prime \}\subset P$, and $\dim \{M\}=\dim \{G/G^\{\prime \}\}$ coincides with the classical definition. Results are obtained concerning the Cartan order of $r$-th order connections that are the product of $r$ first order (Cartan) connections.},
author = {Virsik, Juraj},
journal = {Archivum Mathematicum},
keywords = {non-holonomic jets and connections; semi-holonomic jets and connections; higher order relative; straight and Cartan connections; non-holonomic jets and connections; semi-holonomic jets and connections; higher order derivative; straight and Cartan connections},
language = {eng},
number = {4},
pages = {343-354},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Higher order Cartan connections},
url = {http://eudml.org/doc/18475},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Virsik, Juraj
TI - Higher order Cartan connections
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 4
SP - 343
EP - 354
AB - A Cartan connection associated with a pair $P(M,G^{\prime })\subset P(M,G)$ is defined in the usual manner except that only the injectivity of $\omega :T(P^{\prime })\rightarrow T(G)_{e}$ is required. For an $r$-th order connection associated with a bundle morphism $\Phi :P^{\prime }\rightarrow P$ the concept of Cartan order $q\le r$ is defined, which for $q=r=1, \Phi :P^{\prime }\subset P$, and $\dim {M}=\dim {G/G^{\prime }}$ coincides with the classical definition. Results are obtained concerning the Cartan order of $r$-th order connections that are the product of $r$ first order (Cartan) connections.
LA - eng
KW - non-holonomic jets and connections; semi-holonomic jets and connections; higher order relative; straight and Cartan connections; non-holonomic jets and connections; semi-holonomic jets and connections; higher order derivative; straight and Cartan connections
UR - http://eudml.org/doc/18475
ER -

References

top
  1. Extension du calcul des jets aux jets non holonomes, C.R.A.S. Paris 239(1954), 1762–1764. Zbl0057.15603MR0066734
  2. Sur les connexions d’ordre supérieur, Atti Cong. Un. Mat. Italiana, Pavia-Torino, 1956, 326–328. 
  3. Transformation groups in differential geometry, Ergebnisse der Mathematik 70, Springer Verlag, 1972. Zbl0829.53023MR0355886
  4. Foundations of differential geometry, Vol. 1, Wiley-Interscience, 1963. MR0152974
  5. Some higher order operations with connections, Czech. Math. J. 24(99) (1974), 311–330. Zbl0273.53026MR0356114
  6. On some operations with connections, Math. Nachrichten 69(1975), 297–306. Zbl0318.53034MR0391157
  7. Natural Operations in Differential Geometry, Springer-Verlag, 1993. Zbl0782.53013MR1202431
  8. Total connections in Lie groupoids, Arch. Math. (Brno) 31 (1995), 183-200. (1995) Zbl0841.53024MR1368257
  9. Bunch connections, Diff. Geom. and Applications, Proc. Conf. 1995, Brno, Czech republic, Masaryk University, Brno (1996), 215-229. Zbl0864.53017MR1406340

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.