Holonomy of sub-Riemannian manifolds
Data
1997-05-01
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Artigo
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Resumo
A sub-Riemannian manifold is a smooth manifold which carries a distribution equipped with a metric. We study the holonomy and the horizontal holonomy (i.e. holonomy spanned by loops everywhere tangent to the distribution) of sub-Riemannian manifolds of contact type relative to an adapted connection. in particular, we obtain an Ambrose-Singer type theorem for the horizontal holonomy and we classify the holonomy irreducible sub-Riemannian symmetric spaces (i.e. homogeneous sub-Riemannian manifolds admitting an involutive isometry whose restriction to the distribution is a central symmetry).
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Citação
International Journal of Mathematics. Singapore: World Scientific Publ Co Pte Ltd, v. 8, n. 3, p. 317-344, 1997.