Curvature of matrix and reductive Lie groups
Differential Geometry
2021-08-03 v1 Algebraic Geometry
Representation Theory
Abstract
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 reductive Lie group. We also discuss the relation between commuting matrices and zero sectional curvature.
Keywords
Cite
@article{arxiv.2108.00651,
title = {Curvature of matrix and reductive Lie groups},
author = {Luyining Gan and Ming Liao and Tin-Yau Tam},
journal= {arXiv preprint arXiv:2108.00651},
year = {2021}
}
Comments
11 pages; the final version is published in Journal of Lie Theory