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arXiv · 2102.06327

The Alekseevskii Conjecture in 9 and 10 dimensions

Rohin Berichon
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Abstract

We show that noncompact homogeneous spaces not diffeomorphic to Euclidean space of dimension 9 or 10 admit no homogeneous Einstein metrics of negative Ricci curvature, with only three potential exceptions. The main ingredient in the proof is to show, via a cohomogeneity-one approach, that noncompact homogeneous spaces admitting an ideal isomorphic to $ \mathfrak{sl}_2(\mathbb{R}) $ admit no homogeneous Einstein metrics of negative Ricci curvature.

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Rohin Berichon. 2021-02-12. The Alekseevskii Conjecture in 9 and 10 dimensions. https://doi.org/10.1016/j.difgeo.2021.101782

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