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  • Print publication year: 2019
  • Online publication date: October 2019

3 - Sub-Riemannian Structures


In this chapter we introduce the fundamental object of this book: the sub-Riemannian distance. We prove its finiteness and continuity (Rashevskii–Chow theorem) and the existence of length-minimizers. We then introduce Pontryagin extremals, which are curves in the cotangent space satisfying a first-order necessary condition of length-minimality.

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