## Sub-Riemannian Geometry (Google eBook)André Bellaïche, Jean-Jaques Risler Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: |

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### Contents

1 | |

10 | |

Two examples | 23 |

Privileged coordinates | 30 |

The tangent nilpotent Lie algebra and the algebraic structure | 43 |

Gromovs notion of tangent space | 54 |

Why is the tangent space a group? | 73 |

MIKHAEL GROMOV | 82 |

Anisotropic connections | 302 |

Survey of singular geodesics | 325 |

The example and its properties | 331 |

Note in proof | 337 |

abnormal subRiemannian minimizers | 341 |

Abnormal extremals in dimension 4 | 351 |

An optimality lemma | 357 |

Conclusion | 363 |

Basic definitions examples and problems | 85 |

Horizontal curves and small CC balls | 112 |

Hypersurfaces in CC spaces | 152 |

CarnotCaratheodory geometry of contact manifolds | 196 |

Pfaffian geometry in the internal light | 234 |