Geodesic
Ehresmann connection for the canonical foliation on a~manifold over a~local algebra
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 303-310.

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For a canonical foliation on a manifold $M^{\mathbb A}$ over a local algebra, the $\mathbb A$-affine horizontal distribution complementary to the leaves, similar to the horizontal distribution of a higher order connection on the fiber bundle of $\mathbb A$-jets, is defined. In the case of a complete manifold $M^{\mathbb A}$, the $\mathbb A$-affine horizontal distribution is proved to be an Ehresmann connection in the sense of Blumental–Hebda. It is shown that the $\mathbb A$-affine horizontal distribution on $M^{\mathbb A}$ exists if and only if the Atiyah class of a certain foliated principal bundle vanishes. 
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V. V. Shurygin. Ehresmann connection for the canonical foliation on a~manifold over a~local algebra. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 303-310. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a15/

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