Mathematische Annalen

, Volume 367, Issue 1–2, pp 283–309 | Cite as

The Alekseevskii conjecture in low dimensions

  • Romina M. Arroyo
  • Ramiro A. LafuenteEmail author


The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G / K of negative scalar curvature must be diffeomorphic to \({\mathbb R}^n\). This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.



It is our pleasure to thank Jorge Lauret for fruitful discussions, and Christoph Böhm for providing useful comments on a draft version of this article. Part of this research was carried out while the first author was a visitor at McMaster University. She is very grateful to the Department of Mathematics, the Geometry and Topology group and especially to McKenzie Wang for his kindness and hospitality.


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Authors and Affiliations

  1. 1.FaMAF and CIEMUniversidad Nacional de CórdobaCórdobaArgentina
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany

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