Non Naturally Reductive Einstein Metrics on the Orthogonal Group via Real Flag Manifolds

We obtain new invariant Einstein metrics on the compact Lie groups SO ( n ) which are not naturally reductive. This is achieved by using the real flag manifolds SO ( k 1 + ⋯ + k p ) / SO ( k 1 ) × ⋯ × SO ( k p ) and by imposing certain symmetry assumptions in the set of all left-invariant metrics on...

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Bibliographic Details
Published in:Resultate der Mathematik 2024-02, Vol.79 (1), Article 42
Main Authors: Arvanitoyeorgos, Andreas, Sakane, Yusuke, Statha, Marina
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We obtain new invariant Einstein metrics on the compact Lie groups SO ( n ) which are not naturally reductive. This is achieved by using the real flag manifolds SO ( k 1 + ⋯ + k p ) / SO ( k 1 ) × ⋯ × SO ( k p ) and by imposing certain symmetry assumptions in the set of all left-invariant metrics on SO ( n ) .
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-02068-1