Abstract
For a canonical foliation on a manifoldM A over a local algebra, theA-affine horizontal distribution complementary to the leaves, similar to the horizontal distribution of a higher order connection on the fiber bundle ofA-jets, is defined. In the case of a complete manifoldM A, theA-affine horizontal distribution is proved to be an Ehresmann connection in the sense of Blumental-Hebda. It is shown that theA-affine horizontal distribution onM A exists if and only if the Atiyah class of a certain foliated principal bundle vanishes.
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Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 303–310, February, 1996.
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Shurygin, V.V. Ehresmann connection for the canonical foliation on a manifold over a local algebra. Math Notes 59, 213–218 (1996). https://doi.org/10.1007/BF02310963
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DOI: https://doi.org/10.1007/BF02310963