Natural operators on frame bundles

Krupka, Michal. "Natural operators on frame bundles." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 121-129. <http://eudml.org/doc/221792>.

@inProceedings{Krupka2000,
abstract = {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!},
author = {Krupka, Michal},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {121-129},
publisher = {Circolo Matematico di Palermo},
title = {Natural operators on frame bundles},
url = {http://eudml.org/doc/221792},
year = {2000},
}

TY - CLSWK
AU - Krupka, Michal
TI - Natural operators on frame bundles
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 121
EP - 129
AB - 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!
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221792
ER -