La conjetura de Alekseevskii en dimensiones bajas

ROMINA M. ARROYO; RAMIRO A. LAFUENTE

Santa Fé

Congreso; Reunion Anual de la Union Matematica Argentina; 2015

Universidad Nacional del Litoral

The long-standing Alekseevskii conjecture states that a connected homogeneousEinstein 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.