Geodesic
The natural operators lifting $1$-forms to some vector bundle functors
J. Kurek 1   ; W. M. Mikulski 2
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $F$.
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

J. Kurek  1   ; W. M. Mikulski  2

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 
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     title = {The natural operators lifting $1$-forms
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J. Kurek; W. M. Mikulski. The natural operators lifting $1$-forms
 to some vector bundle functors. Colloquium Mathematicum, Tome 93 (2002) no. 2, pp. 259-265. doi: 10.4064/cm93-2-5

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