Natural operators lifting vector fields on manifolds to the bundles of covelocities

Mikulski, W. M.. "Natural operators lifting vector fields on manifolds to the bundles of covelocities." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1996. [105]-121. <http://eudml.org/doc/221839>.

@inProceedings{Mikulski1996,
abstract = {The author proves that for a manifold $M$ of dimension greater than 2 the sets of all natural operators $TM \rightarrow (T^\{r*\}_k M, T^\{q*\}_\ell M)$ and $TM \rightarrow TT^\{r*\}_k M$, respectively, are free finitely generated $C^\infty ((\mathbb \{R\}^k)^r)$-modules. The space $T^\{r*\}_k M = J^r(M, \mathbb \{R\}^k)_0$, this is, jets with target 0 of maps from $M$ to $\mathbb \{R\}^k$, is called the space of all $(k,r)$-covelocities on $M$. Examples of such operators are shown and the bases of the modules are explicitly constructed. The definitions and methods are those of the book of I. Kolář, P. W. Michor and J. Slovák [Natural operations in differential geometry, Springer-Verlag, Berlin (1993; Zbl 0782.53013)].},
author = {Mikulski, W. M.},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Physics; Winter school; Srní(Czech Republic)},
location = {Palermo},
pages = {[105]-121},
publisher = {Circolo Matematico di Palermo},
title = {Natural operators lifting vector fields on manifolds to the bundles of covelocities},
url = {http://eudml.org/doc/221839},
year = {1996},
}

TY - CLSWK
AU - Mikulski, W. M.
TI - Natural operators lifting vector fields on manifolds to the bundles of covelocities
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1996
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [105]
EP - 121
AB - The author proves that for a manifold $M$ of dimension greater than 2 the sets of all natural operators $TM \rightarrow (T^{r*}_k M, T^{q*}_\ell M)$ and $TM \rightarrow TT^{r*}_k M$, respectively, are free finitely generated $C^\infty ((\mathbb {R}^k)^r)$-modules. The space $T^{r*}_k M = J^r(M, \mathbb {R}^k)_0$, this is, jets with target 0 of maps from $M$ to $\mathbb {R}^k$, is called the space of all $(k,r)$-covelocities on $M$. Examples of such operators are shown and the bases of the modules are explicitly constructed. The definitions and methods are those of the book of I. Kolář, P. W. Michor and J. Slovák [Natural operations in differential geometry, Springer-Verlag, Berlin (1993; Zbl 0782.53013)].
KW - Proceedings; Geometry; Physics; Winter school; Srní(Czech Republic)
UR - http://eudml.org/doc/221839
ER -