2015/03/24 by Romina M. Arroyo, Arroyo, Romina M., R Lafuente +2 · 1 citation
Mathematics · Physics and Astronomy · #53C25 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C25 #msc:53C30
paper · pdf · doi:10.48550/arxiv.1503.07079
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
openalex publication_date 2015/03/24 · arxiv created 2016/02/19 · arxiv updated 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G/K of negative scalar curvature must be diffeomorphic to Rn. 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.