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arXiv · 1503.07079

The Alekseevskii conjecture in low dimensions

Romina M. Arroyo·Ramiro A. Lafuente
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Abstract

The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G/K of negative scalar curvature must be diffeomorphic to 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.

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Romina M. Arroyo, Ramiro A. Lafuente. 2015-03-24. The Alekseevskii conjecture in low dimensions. https://arxiv.org/abs/1503.07079

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