The Alekseevskii conjecture in low dimensions
Differential Geometry
2016-02-22 v2
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.
Cite
@article{arxiv.1503.07079,
title = {The Alekseevskii conjecture in low dimensions},
author = {Romina M. Arroyo and Ramiro A. Lafuente},
journal= {arXiv preprint arXiv:1503.07079},
year = {2016}
}
Comments
20 pages, 1 table; v2: The structure results in Section 2 have been substantially improved, and some new applications of them were added. To appear in Mathematische Annalen