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arXiv · 0904.0104

Einstein metrics on compact Lie groups which are not naturally reductive

Andreas Arvanitoyeorgos·Kunihiko Mori·Yusuke Sakane
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Abstract

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by J. E. D'Atri and W. Ziller in 1979. In 1996 the second author obtained non-naturally reductive Einstein metrics on the Lie group SU(n) for $n \ge 6$, by using a method of Riemannian submersions. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) ($n \geq 11$), $Sp(n)$ ($n \geq 3$), $E_6$, $E_7$, and $E_8$.

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Andreas Arvanitoyeorgos, Kunihiko Mori, Yusuke Sakane. 2009-04-01. Einstein metrics on compact Lie groups which are not naturally reductive. https://arxiv.org/abs/0904.0104

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