| Summary:
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The author proves that for a manifold $M$ of dimension greater than 2 the sets of all natural operators $TM \to (T^{r*}_k M, T^{q*}_\ell M)$ and $TM \to TT^{r*}_k M$, respectively, are free finitely generated $C^\infty ((\bbfR^k)^r)$-modules. The space $T^{r*}_k M = J^r(M, \bbfR^k)_0$, this is, jets with target 0 of maps from $M$ to $\bbfR^k$, 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 {\it I. Kol\'a\v{r}, P. W. Michor} and {\it J. Slov\'ak} [Natural operations in differential geometry, Springer-Verlag, Berlin (1993; Zbl 0782.53013)]. (English) |
