The natural operators lifting horizontal $1$-forms to some vector bundle functors on fibered manifolds

Tom 97 / 2003

J. Kurek, W. M. Mikulski Colloquium Mathematicum 97 (2003), 141-149 MSC: Primary 58A20. DOI: 10.4064/cm97-2-1

Streszczenie

Let $F:{\mathcal F}{\mathcal M}\rightarrow {\mathcal V}{\mathcal B}$ be a vector bundle functor. First we classify all natural operators $T_{{\rm proj}| {\mathcal F}{\mathcal M}_{m,n}}\rightsquigarrow T^{(0,0)} (F_{| {\mathcal F}{\mathcal M}_{m,n}})^*$ transforming projectable vector fields on $Y$ to functions on the dual bundle $(FY)^*$ for any ${\mathcal F}{\mathcal M}_{m,n}$-object $Y$. Next, under some assumption on $F$ we study natural operators $T^*_{{\rm hor} | {\mathcal F}{\mathcal M}_{m,n}}\rightsquigarrow T^*(F_{| {\mathcal F}{\mathcal M}_{m,n}})^*$ lifting horizontal $1$-forms on $Y$ to $1$-forms on $(FY)^*$ for any $Y$ as above. As an application we classify natural operators $T^*_{{\rm hor}| {\mathcal F}{\mathcal M}_{m,n}}\rightsquigarrow T^*(F_{| {\mathcal F}{\mathcal M}_{m,n}})^*$ for some vector bundle functors $F$ on fibered manifolds.

Autorzy

  • J. KurekInstitute of Mathematics
    Maria Curie-Skłodowska University
    Pl. Marii Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail
  • W. M. MikulskiInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
    e-mail

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