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Constant curvature models in sub-Riemannian geometry. (English) Zbl 0854.53033
A sub-Riemannian manifold is a differential manifold together with a smooth distribution of planes which carries a metric. We define a canonical connection on a sub-Riemannian manifold analogous to the Levi-Civita connection for Riemannian manifolds. We state a classification theorem for sub-Riemannian manifolds of constant sectional curvature and vanishing torsion in dimension 3. The higher dimensional classification is completed in the authors’ paper [The equivalence problem in sub-Riemannian geometry, preprint (1993; per bibl.)].

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C10 \(G\)-structures