The natural operators $T_{\vert{\cal M} f_n}\rightsquigarrow T^*T^{r*}$ and $T_{\vert {\cal M} f_n}\rightsquigarrow {\mit\Lambda}^2T^ *T^{r*}$
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 55-65
MSC: Primary 58A20.
DOI: 10.4064/cm93-1-6
Abstract
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.
