The natural operators lifting $1$-forms to some vector bundle functors

J. Kurek¹ ; W. M. Mikulski²

¹ Institute of Mathematics Maria Curie-Skłodowska University Pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
² Institute of Mathematics Jagiellonian University Reymonta 4 50-039 Kraków, Poland

Colloquium Mathematicum, Tome 93 (2002) no. 2, pp. 259-265

Résumé

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 $F$.

Détail

DOI : 10.4064/cm93-2-5

Keywords: cal cal cal vector bundle functor first classify natural operators cal rightsquigarrow cal * transforming vector fields functions dual bundle functor cal * study natural operators * cal rightsquigarrow * cal * lifting forms cal * application classify natural operators * cal rightsquigarrow * cal * known vector bundle functors