*Published Paper*

**Inserted:** 18 jan 2017

**Last Updated:** 11 sep 2017

**Journal:** Analysis and Geometry in Metric Spaces

**Volume:** 5

**Number:** 1

**Pages:** 47--68

**Year:** 2017

**Abstract:**

The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on $RCD^{*}(K,N)$ metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.

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