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.
@article{bwmeta1.element.doi-10_1515_agms-2017-0003,
author = {Bang-Xian Han and Andrea Mondino},
title = {Angles between Curves in Metric Measure Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {5},
year = {2017},
pages = {47-68},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0003}
}
Bang-Xian Han; Andrea Mondino. Angles between Curves in Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 5 (2017) pp. 47-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0003/