Natural operators on frame bundles

Krupka, Michal

Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), p. 121-129 / Harvested from

Résumé

Let $F_{1}$ be a natural bundle of order $r_{1}$ ; a basis of the $s$ -th order differential operators of $F_{1}$ with values in $r_{2}$ -th order bundles is an operator $D$ of that type such that any other one is obtained by composing $D$ with a suitable zero-order operator. In this article a basis is found in the following two cases: for $F_{1} = semi F^{r_{1}}$ (semi-holonomic $r_{1}$ -th order frame bundle), $s = 0$ , $r_{2} < r_{1}$ and $F_{1} = F^{1}$ ( $1$ -st order frame bundle), $r_{2} \leq s$ . The author uses here the so-called method of orbit reduction which provides one with a criterion for checking a basis in terms of the $K_{n}^{r_{1} + s, r_{2}}$ -action on the type fiber of the concerned bundle, where $K_{n}^{r_{1} + s, r_{2}}$ denotes the kernel of the projection of the $(n, r_{1} + s)$ jet group onto the $(n, r_{2})$ jet group [see I. Kolár, P. Michor and J. Slovák, ‘Natural operations in differential geometry’ (Springer-Verlag, Berlin) (1993; Zbl 0782.53013) or D. Krupka, Loc!

MR MR1758087 | Zbl 0971.58002

EUDML-ID : urn:eudml:doc:221792
Mots clés:

@article{701655,
     title = {Natural  operators on frame bundles},
     booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2000},
     pages = {121-129},
     mrnumber = {MR1758087},
     zbl = {0971.58002},
     url = {http://dml.mathdoc.fr/item/701655}
}

Krupka, Michal. Natural  operators on frame bundles, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books,  (2000), pp. 121-129. http://gdmltest.u-ga.fr/item/701655/