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On lifting of connections to Weil bundles

Tom 103 / 2012

Jan Kurek, Włodzimierz M. Mikulski Annales Polonici Mathematici 103 (2012), 319-324 MSC: Primary 58A32; Secondary 58A20. DOI: 10.4064/ap103-3-7

Streszczenie

We prove that the problem of finding all $\mathcal M f_m$-natural operators $B:Q\rightsquigarrow QT^A$ lifting classical linear connections $\nabla$ on $m$-manifolds $M$ to classical linear connections $B_M(\nabla)$ on the Weil bundle $T^AM$ corresponding to a $p$-dimensional (over $\mathbb R$) Weil algebra $A$ is equivalent to the one of finding all $\mathcal M f_m$-natural operators $C:Q\rightsquigarrow (T^1_{p-1},T^*\otimes T^*\otimes T)$ transforming classical linear connections $\nabla$ on $m$-manifolds $M$ into base-preserving fibred maps $C_M(\nabla):T^1_{p-1}M=\bigoplus^{p-1}_MTM\to T^*M\otimes T^*M\otimes TM$.

Autorzy

  • Jan KurekInstitute of Mathematics
    Maria Curie-Skłodowska University
    Pl. Marii Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail
  • Włodzimierz M. MikulskiChair of Geometry
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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