A remark on left invariant metrics on compact Lie groups

Details A remark on left invariant metrics on compact Lie groups A remark on left invariant metrics on compact Lie groups

2007-05-07

arxiv.org/abs/0705.0985v1

Mathematics

Differential Geometry

4 pages

Scientific paper

We show that a left invariant metric on a compact Lie group $G$ which is
obtained by stretching a biinvariant metric in the direction of a subalgebra
$\h$ of $\g$ always has some negative sectional curvature, unless the
semi-simple part of $\h$ is an ideal of $\g$.

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