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math.DG2024
Geometric Properties and Distance Inequalities on Grassmannians
Tin-Yau Tam, Xiang Xiang Wang
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 ma…
math.DG2021
Curvature of matrix and reductive Lie groups
Luyining Gan, Ming Liao, Tin-Yau Tam
In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reduc…