English

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