1996 | OriginalPaper | Buchkapitel
The tangent space in sub-Riemannian geometry
verfasst von : André Bellaïche
Erschienen in: Sub-Riemannian Geometry
Verlag: Birkhäuser Basel
Enthalten in: Professional Book Archive
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Tangent spaces of a sub-Riemannian manifold are themselves sub-Riemannian manifolds. They can be defined as metric spaces, using Gromov’s definition of tangent spaces to a metric space, and they turn out to be sub-Riemannian manifolds. Moreover, they come with an algebraic structure: nilpotent Lie groups with dilations. In the classical, Riemannian, case, they are indeed vector spaces, that is, abelian groups with dilations. Actually, the above is true only for regular points. At singular points, instead of nilpotent Lie groups one gets quotient spaces G/H of such groups G.