# Carnot-Carathéodory spaces seen from within

@inproceedings{Gromov1996CarnotCarathodorySS,
title={Carnot-Carath{\'e}odory spaces seen from within},
author={M. Gromov},
year={1996}
}
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 $$c\, \in \,\mathcal{H} \Leftrightarrow \,{c_i} \in \mathcal{H},\,i = 1, \ldots ,k.$$
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