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

7 - Lie Groups and Left-Invariant Sub-Riemannian Structures


In this chapter we study normal Pontryagin extremals on left-invariant sub-Riemannian structures on a Lie group $G$. Such structures provide most of the examples in which normal Pontryagin extremals can be computed explicitly in terms of elementary functions. We introduce Lie groups by studying subgroups of the group of diffeomorphisms of a manifold $M$ induced by a family of vector fields whose Lie algebra is finite dimensional.