A remark on left invariant metrics on compact Lie groups

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

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Bibliographic Details
Published in:Archiv der Mathematik 2008-02, Vol.90 (2), p.158-162
Main Author: Schwachhöfer, Lorenz J.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Description
Summary:. We show that a left invariant metric on a compact Lie group G with Lie algebra has some negative sectional curvature if it is obtained by enlarging a biinvariant metric on a subalgebra , unless the semi-simple part of is an ideal of This answers a question raised in [8].
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-007-2433-7