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 \(\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)\) and by imposing certain symmetry assumptions in the set of all left-invariant...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Arvanitoyeorgos, Andreas, Sakane, Yusuke, Statha, Marina
Format: Article
Language:English
Subjects:
Flags
Invariants
Lie groups
Manifolds
Online Access:Get full text
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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 \(\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)\) and by imposing certain symmetry assumptions in the set of all left-invariant metrics on \(\SO(n)\).
ISSN:2331-8422
DOI:10.48550/arxiv.2409.18990