Geodesic
The natural operators $T_{\vert{\cal M} f_n}\rightsquigarrow T^*T^{r*}$ and $T_{\vert {\cal M} f_n}\rightsquigarrow {\mit\Lambda}^2T^ *T^{r*}$
W. M. Mikulski1
1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Colloquium Mathematicum, Tome 93 (2002) no. 1, pp. 55-65

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Let $r$ and $n$ be natural numbers. For $n\geq 2$ all natural operators $T_{| {\cal M} f_n}\rightsquigarrow T^*T^{r*}$ transforming vector fields on $n$-manifolds $M$ to $1$-forms on $T^{r*}M=J^r(M,{\mathbb R})_0$ are classified. For $n\geq 3$ all natural operators $T_{| {\cal M} f_n}\rightsquigarrow {\mit \Lambda }^2T^*T^{r*}$ transforming vector fields on $n$-manifolds $M$ to $2$-forms on $T^{r*}M$ are completely described.
DOI : 10.4064/cm93-1-6
Keywords: natural numbers geq natural operators cal rightsquigarrow *t r* transforming vector fields n manifolds forms r* m mathbb classified geq natural operators cal rightsquigarrow mit lambda *t r* transforming vector fields n manifolds forms r* completely described

W. M. Mikulski 1

1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland 
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and $T_{\vert {\cal M} f_n}\rightsquigarrow {\mit\Lambda}^2T^
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W. M. Mikulski. The natural operators
$T_{\vert{\cal M} f_n}\rightsquigarrow T^*T^{r*}$
and $T_{\vert {\cal M} f_n}\rightsquigarrow {\mit\Lambda}^2T^
*T^{r*}$. Colloquium Mathematicum, Tome 93 (2002) no. 1, pp. 55-65. doi: 10.4064/cm93-1-6

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