Higher order linear connections from first order ones

Włodzimierz M. Mikulski

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 4, page 285-288
  • ISSN: 0044-8753

Abstract

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We describe how find all f m -natural operators D transforming torsion free classical linear connections on m -manifolds M into r -th order linear connections D ( ) on M .

How to cite

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Mikulski, Włodzimierz M.. "Higher order linear connections from first order ones." Archivum Mathematicum 043.4 (2007): 285-288. <http://eudml.org/doc/250157>.

@article{Mikulski2007,
abstract = {We describe how find all $\mathcal \{M\}f_m$-natural operators $D$ transforming torsion free classical linear connections $\nabla $ on $m$-manifolds $M$ into $r$-th order linear connections $D(\nabla )$ on $M$.},
author = {Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {higher order linear connection; natural operator; higher order linear connection; natural operator},
language = {eng},
number = {4},
pages = {285-288},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Higher order linear connections from first order ones},
url = {http://eudml.org/doc/250157},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Higher order linear connections from first order ones
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 4
SP - 285
EP - 288
AB - We describe how find all $\mathcal {M}f_m$-natural operators $D$ transforming torsion free classical linear connections $\nabla $ on $m$-manifolds $M$ into $r$-th order linear connections $D(\nabla )$ on $M$.
LA - eng
KW - higher order linear connection; natural operator; higher order linear connection; natural operator
UR - http://eudml.org/doc/250157
ER -

References

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  1. Kolář I., Torsion-free connections on higher order frame bundles, in New Development in Differential Geometry, Proceedings (Conference in Debrecen), Kluwer 1996, 233–241. (1996) MR1377287
  2. Kolář I., On the torsion-free connections on higher order frame bundles, Publ. Math. Debrecen 67 (3-4), (2005), 373–379. Zbl1083.53026MR2162129
  3. Kolář I., Michor P. W., Slovák J., Natural Operations In Differential Geometry, Springer-Verlag Berlin 1993. (1993) Zbl0782.53013MR1202431
  4. Paluszny M., Zajtz A., Foundations of differential geometry of natural bundles, Lecture Notes Univ. Caracas, 1984. (1984) 

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