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The tangent space in sub-Riemannian geometry

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Book cover Sub-Riemannian Geometry

Part of the book series: Progress in Mathematics ((PM,volume 144))

Abstract

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.

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris 7-Denis Diderot, 2, place Jussieu, 75251, Paris 5e, France

    André Bellaïche

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  1. André Bellaïche
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Editors and Affiliations

  1. Departement de Mathématiques, Université Paris 7 — Denis Diderot, 2, place Jussieu, F-75251, Paris 5e, France

    André Bellaïche

  2. Université Paris VI — Pierre et Marie Curie, F-75252, Paris 5e, France

    Jean-Jacques Risler

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Bellaïche, A. (1996). The tangent space in sub-Riemannian geometry. In: Bellaïche, A., Risler, JJ. (eds) Sub-Riemannian Geometry. Progress in Mathematics, vol 144. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9210-0_1

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  • DOI: https://doi.org/10.1007/978-3-0348-9210-0_1

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9946-8

  • Online ISBN: 978-3-0348-9210-0

  • eBook Packages: Springer Book Archive

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