Natural operators in the view of Cartan geometries
Archivum Mathematicum (2003)
- Volume: 039, Issue: 1, page 57-75
- ISSN: 0044-8753
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topPanák, Martin. "Natural operators in the view of Cartan geometries." Archivum Mathematicum 039.1 (2003): 57-75. <http://eudml.org/doc/249142>.
@article{Panák2003,
abstract = {We prove, that $r$-th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1,0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r-1$. On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for the reductive and torsion free geometries.},
author = {Panák, Martin},
journal = {Archivum Mathematicum},
keywords = {Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry},
language = {eng},
number = {1},
pages = {57-75},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Natural operators in the view of Cartan geometries},
url = {http://eudml.org/doc/249142},
volume = {039},
year = {2003},
}
TY - JOUR
AU - Panák, Martin
TI - Natural operators in the view of Cartan geometries
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 1
SP - 57
EP - 75
AB - We prove, that $r$-th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1,0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r-1$. On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for the reductive and torsion free geometries.
LA - eng
KW - Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry
UR - http://eudml.org/doc/249142
ER -
References
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