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

Mikulski, W. M.

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1996), p. [105]-121 / Harvested from

Résumé

The author proves that for a manifold $M$ of dimension greater than 2 the sets of all natural operators $T M \to (T_{k}^{r *} M, T_{ℓ}^{q *} M)$ and $T M \to T T_{k}^{r *} M$ , respectively, are free finitely generated $C^{\infty} ({(ℝ^{k})}^{r})$ -modules. The space $T_{k}^{r *} M = J^{r} {(M, ℝ^{k})}_{0}$ , this is, jets with target 0 of maps from $M$ to $ℝ^{k}$ , 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)].

MR MR1396605 | Zbl 0854.58006

EUDML-ID : urn:eudml:doc:221839
Mots clés:

@article{701568,
     title = {Natural operators lifting vector fields on manifolds to the bundles of covelocities},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1996},
     pages = {[105]-121},
     mrnumber = {MR1396605},
     zbl = {0854.58006},
     url = {http://dml.mathdoc.fr/item/701568}
}

Mikulski, W. M. Natural operators lifting vector fields on manifolds to the bundles of covelocities, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1996), pp. [105]-121. http://gdmltest.u-ga.fr/item/701568/