E-mail: mikulski@im.uj.edu.pl
Abstract. For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r),a}$ over $n$-manifolds such that $T^{(r),0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$. For integers $r\geq 1$ and $n\geq 3$ and a real number $a<0$ we classify all natural operators $T_{\vert \Cal M_n}\rightsquigarrow TT^{(r),a}$ lifting vector fields from $n$-manifolds to $T^{(r),a}$.
AMSclassification. 58A20, 53A55
Keywords. Natural bundle, natural transformation, natural operator