Geometric Properties and Distance Inequalities on Grassmannians
Differential Geometry
2024-12-20 v1
Abstract
In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities.
Keywords
Cite
@article{arxiv.2412.15161,
title = {Geometric Properties and Distance Inequalities on Grassmannians},
author = {Tin-Yau Tam and Xiang Xiang Wang},
journal= {arXiv preprint arXiv:2412.15161},
year = {2024}
}