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1 results

  • 17 - Curvature in 3D Contact Sub-RiemannianGeometry

  • Andrei Agrachev, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Davide Barilari, Université de Paris VII (Denis Diderot), Ugo Boscain, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book:
    A Comprehensive Introduction to Sub-Riemannian Geometry
    Published online:
    28 October 2019
    Print publication:
    31 October 2019, pp 571-606

  • Summary

    In this chapter we discuss the notion of curvature insub-Riemannian geometry. We will consider inparticular the case of three-dimensional contactmanifolds, which reduces to two functionalinvariants that are constant for left-invariantstructures on Lie groups. The final part of thechapter is then devoted to the classification ofleft-invariant structures on three-dimensional Liegroups, with respect to local isometries anddilations, in terms of the above invariants.