Geodesic
Bundles with multivalued automorphism groups
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 600-616 Cet article a éte moissonné depuis la source Math-Net.Ru

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A category whose objects are principal bundles with fixed base (smooth manifold) $B$, structure group $T^k$, and finite group $\Delta$ of multivalued automorphisms is constructed; the morphisms are required to be equivariant with respect to $\Delta$. Invariants are found and used to calculate the group of equivalence classes of the category objects. Examples are given and applications to dynamical systems with gyroscopic forces are suggested. 
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A. V. Ryzhkova; E. I. Yakovlev. Bundles with multivalued automorphism groups. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 600-616. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a12/

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