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

9 - 2D Almost-Riemannian Structures


Almost-Riemannian structures form prototypes for rank-varying sub-Riemannian structures. In this chapter we study the two-dimensional case, which is very simple since it is Riemannian almost everywhere but even so presents some interesting phenomena such as the presence of sets of finite diameter but infinite area. Also, the Gauss–Bonnet theorem has a surprising form in this context.