Torsion-free connections on higher order frame bundles

  • Ivan Kolář
Part of the Mathematics and Its Applications book series (MAIA, volume 350)


We deduce that torsion-free connections on the r-th order frame bundle P r M of a manifold M can be identified with certain reductions of P r+1 M. They are also interpreted as splittings of T*M into the bundle of all (1,r+l)-covelocities on M. Finally we determine all natural operators transforming torsion-free connections on P 1 M into torsion-free connections on P 2 M.


Principal Bundle Natural Operator Frame Bundle Exponential Operator Canonical Bijection 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Ivan Kolář
    • 1
  1. 1.Department of Algebra and Geometry Faculty of ScienceMasaryk UniversityBrnoCzech Republic

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