Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500014 | Journal of Geometry and Physics | 2017 | 34 Pages |
Abstract
Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Gröbner bases and classify the real solutions of the associated algebraic systems. For the Lie group G2 we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E7 and E8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K)-invariant by different Lie subgroups K.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Ioannis Chrysikos, Yusuke Sakane,