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

17 - Curvature in 3D Contact Sub-Riemannian Geometry

Summary

In this chapter we discuss the notion of curvature in sub-Riemannian geometry. We will consider in particular the case of three-dimensional contact manifolds, which reduces to two functional invariants that are constant for left-invariant structures on Lie groups. The final part of the chapter is then devoted to the classification of left-invariant structures on three-dimensional Lie groups, with respect to local isometries and dilations, in terms of the above invariants.

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