Czechoslovak Mathematical Journal, Vol. 53, No. 4, pp. 949-962, 2003

# Torsions of connections on higher order cotangent bundles

## Miroslav Doupovec, Jan Kurek

M. Doupovec, Department of Mathematics, FSI VUT Brno, Technicka 2, 616 69 Brno, Czech Republic, e-mail: doupovec@um.fme.vutbr.cz; J. Kurek, Institute of Mathematics, Maria Curie-Sklodowska University, Plac Marii Curie-Sklodowskej 1, 20-031 Lublin, Poland, e-mail: kurek@golem.umcs.pl

Abstract: By a torsion of a general connection $\Gamma$ on a fibered manifold $Y\to M$ we understand the Frolicher-Nijenhuis bracket of $\Gamma$ and some canonical tangent valued one-form (affinor) on $Y$. Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.

Keywords: affinor, general connection, torsion

Classification (MSC 2000): 53C05, 58A20

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