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arXiv · 1612.02227

On left-invariant Einstein Riemannian metrics that are not geodesic orbit

Yu. G. Nikonorov
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Abstract

In this paper we prove that the compact Lie group $G_2$ admits a left-invariant Einstein metric that is not geodesic orbit. In order to prove the required assertion, we develop some special tools for geodesic orbit Riemannian manifolds. It should be noted that a suitable metric is discovered in a recent paper by I. Chrysikos and Y. Sakane, where the authors proved also that this metric is not naturally reductive.

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Yu. G. Nikonorov. 2016-12-07. On left-invariant Einstein Riemannian metrics that are not geodesic orbit. https://doi.org/10.1007/s00031-018-9476-7

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