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First neighbourhood of the diagonal, and geometric distributions. (English) Zbl 1073.53020
In the paper under review the notion of geometric distribution on a manifold in terms of its first neighborhood of the diagonal is presented and studied. The main content is a description of the differential-geometric notions of distribution and involutive distribution in “combinatorial” terms, respectively. Furthermore, the author applies these notions, and some specific techniques as well, in order to prove a version of the Ambrose-Singer holonomy theorem.

MSC:
53A55 Differential invariants (local theory), geometric objects
58A10 Differential forms in global analysis
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