A remark on left invariant metrics on compact Lie groups

Abstract

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 $\g$.

4 pages

References in corpus (1)

• Homogeneous Metrics with nonnegative curvature