THE NATURAL OPERATORS LIFTING VECTOR FIELDS TO $(J^rT^*)^*$

Wlodzimierz M. Mikulski

Address. Institute of Mathematics, Jagiellonian University, Krak¢w, Reymonta 4, POLAND

E-mail: Wlodzimierz.Mikulski@im.uj.edu.pl

Abstract. For integers $r\geq 2$ and $n\geq 2$ a complete classification of all natural operators $A:T_{\vert \M_n}\r T(J^rT^*)^*$ lifting vector fields to vector fields on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given.

AMSclassification. 58A20, 53A55

Keywords. Bundle functors, natural transformations, natural operators