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Sub-Riemannian Geometry pp 79–323Cite as

Carnot-Carathéodory spaces seen from within

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Abstract

Let V be a smooth manifold where we distinguish a subset H in the set of all piecewise smooth curves c in V. We assume that H is defined by a local condition on curves, i.e. if c is divided into segments c 1,…, c k , then

$$ c\, \in \,\mathcal{H} \Leftrightarrow \,{c_i} \in \mathcal{H},\,i = 1, \ldots ,k. $$

Keywords

  • Riemannian Manifold
  • Heisenberg Group
  • Hausdorff Dimension
  • Nilpotent Group
  • Homotopy Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

I thank Richard Montgomery for reading the manuscript and locating a multitude of errors.

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  1. Mikhael Gromov
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  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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Gromov, M. (1996). Carnot-Carathéodory spaces seen from within. 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_2

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