A remark on left invariant metrics on compact Lie groups
Differential Geometry
2007-05-23 v1
Abstract
We show that a left invariant metric on a compact Lie group which is obtained by stretching a biinvariant metric in the direction of a subalgebra of always has some negative sectional curvature, unless the semi-simple part of is an ideal of .
Keywords
Cite
@article{arxiv.0705.0985,
title = {A remark on left invariant metrics on compact Lie groups},
author = {Lorenz J. Schwachhoefer},
journal= {arXiv preprint arXiv:0705.0985},
year = {2007}
}