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Title: Natural operators on frame bundles (English)
Author: Krupka, Michal
Language: English
Journal: Proceedings of the 19th Winter School "Geometry and Physics"
Issue: 1999
Pages: 121-129
Category: math
Summary: 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 $F_1=\text{semi} F^{r_1}$ (semi-holonomic $r_1$-th order frame bundle), $s=0$, $r_2<r_1$ and $F_1=F^1$ ($1$-st order frame bundle), $r_2\le s$. 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 $K^{r_1+s,r_2}_n$-action on the type fiber of the concerned bundle, where $K^{r_1+s,r_2}_n$ 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! (English)
MSC: 53A55
MSC: 58A20
MSC: 58A32
idZBL: Zbl 0971.58002
idMR: MR1758087
Date available: 2009-07-13T21:43:39Z
Last updated: 2012-09-18
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