Journal of Lie Theory 30 (2020), No. 2, 361--370
Copyright Heldermann Verlag 2020
Curvature of Matrix and Reductive Lie Groups
Luyining Gan
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A.
lzg0027@auburn.edu
Ming Liao
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A.
liaomin@auburn.edu
Tin-Yau Tam
Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, U.S.A.
ttam@unr.edu
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: Curvature, general linear group, reductive Lie group, closed subgroup.
MSC: 53B20, 14L35, 51N30.
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