Geodesic
Angles between Curves in Metric Measure Spaces
Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 47-68.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : angle, metric measure space, Wasserstein space, curvature dimension condition, Ricci curvature 
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Han, Bang-Xian; Mondino, Andrea. Angles between Curves in Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 47-68. http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a2/