arXiv 1503.070792015-03math.DG

The Alekseevskii conjecture in low dimensions

Romina M. Arroyo, Ramiro A. Lafuente

备注：: 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

英文摘要：

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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