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Session S23 - Group actions in Differential Geometry

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The Alekseevskii Conjecture in 9 and 10 dimensions

Rohin Berichon

University of Queensland, Australia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The study of Einstein Riemannian manifolds is a broad, yet rich field of study. In the case of homogeneous manifolds, Alekseevskii famously conjectured in 1975 that every connected homogeneous Einstein manifold with negative Ricci curvature is diffeomorphic to Euclidean space. Until now, the conjecture was only known up to dimension 8, besides 5 possible exceptions, and in some cases in dimension 10. Our work shows 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.

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