This article is cited in 3 papers

Ehresmann connection for the canonical foliation on a manifold over a local algebra

V. V. Shurygin

Kazan State University

Abstract: 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.

UDC: 514.76

Received: 17.05.1993

DOI: 10.4213/mzm1717

 English version: Mathematical Notes, 1996, 59:2, 213–218

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