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.

中文翻译：

---

公制度量空间中曲线之间的角度

摘要 本文的目的是在度量（和度量）空间的框架内研究两条曲线之间的夹角。更准确地说，我们给出了度量空间中两条曲线之间的角度的新概念。这种概念与最优运输具有自然的相互作用，特别适合满足曲率维条件的度量空间。事实上，主要结果之一是余弦公式在 RCD*(K, N) 度量空间上的有效性。因此，新引入的概念与黎曼流形、Ricci 极限空间和 Alexandrov 空间的相应经典概念兼容。