The natural operators lifting $1$-forms to some vector bundle functors
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 259-265
MSC: Primary 58A20.
DOI: 10.4064/cm93-2-5
Abstract
Let $F:{\cal M} f\to {\cal V}{\cal B}$ be a vector bundle functor. First we classify all natural operators $T_{| {\cal M} f_n}\rightsquigarrow T^{(0,0)} (F_{| {\cal M} f_n})^*$ transforming vector fields to functions on the dual bundle functor $(F_{| {\cal M} f_n})^*$. Next, we study the natural operators $T^*_{| {\cal M} f_n}\rightsquigarrow T^*(F_{| {\cal M} f_n})^*$ lifting $1$-forms to $(F_{| {\cal M} f_n})^*$. As an application we classify the natural operators $T^*_{| {\cal M} f_n}\rightsquigarrow T^*(F_{| {\cal M} f_n})^*$ for some well known vector bundle functors $F$.
