Geodesic
Curvature of Matrix and Reductive Lie Groups
Journal of Lie theory, Tome 30 (2020) no. 2, pp. 361-37
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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.
Classification : 53B20, 14L35, 51N30
Mots-clés : Curvature, general linear group, reductive Lie group, closed subgroup 
@article{JLT_2020_30_2_JLT_2020_30_2_a4,
     author = {L. Gan and M. Liao and T.-Y. Tam},
     title = {Curvature of {Matrix} and {Reductive} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {361--37},
     year = {2020},
     volume = {30},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a4/}
}
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L. Gan; M. Liao; T.-Y. Tam. Curvature of Matrix and Reductive Lie Groups. Journal of Lie theory, Tome 30 (2020) no. 2, pp. 361-37. http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a4/