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Published online by Cambridge University Press: 28 October 2019
Almost-Riemannian structures form prototypes forrank-varying sub-Riemannian structures. In thischapter we study the two-dimensional case, which isvery simple since it is Riemannian almost everywherebut even so presents some interesting phenomena suchas the presence of sets of finite diameter butinfinite area. Also, the Gauss–Bonnet theorem has asurprising form in this context.
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