Abstract
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.
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© 1996 Kluwer Academic Publishers
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Kolář, I. (1996). Torsion-free connections on higher order frame bundles. In: Tamássy, L., Szenthe, J. (eds) New Developments in Differential Geometry. Mathematics and Its Applications, vol 350. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0149-0_18
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DOI: https://doi.org/10.1007/978-94-009-0149-0_18
Publisher Name: Springer, Dordrecht
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