Archiv der Mathematik

, Volume 90, Issue 2, pp 158–162 | Cite as

A remark on left invariant metrics on compact Lie groups

  • Lorenz J. SchwachhöferEmail author


We show that a left invariant metric on a compact Lie group G with Lie algebra \({\mathcal{g}}\) has some negative sectional curvature if it is obtained by enlarging a biinvariant metric on a subalgebra \({\mathcal{h}} \subset {\mathcal{g}}\), unless the semi-simple part of \({\mathcal{h}}\) is an ideal of \({\mathcal{g}}.\) This answers a question raised in [8].

Mathematics Subject Classification (2000).

53C20 53C30 


Left invariant metrics non-negative sectional curvature 


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Copyright information

©  2008

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität DortmundDortmundGermany

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