Homogeneous Ricci solitons in low dimensions

ROMINA M. ARROYO; RAMIRO A. LAFUENTE

Chapel Hill, North Carolina

Congreso; Group actions in Riemannian geometry; 2014

One of the most important open problems on Einstein homogeneous manifolds is "Alekseevskii´s conjecture". This conjecture says that any homogeneous Einstein space of negative scalar curvature is diffeomorphic to a Euclidean space. Due to recent results of Lafuente - Lauret and Jablonski, this conjecture is equivalent to the analogous statement for algebraic solitons, which we call "Generalized Alekseevskii´s conjecture". The aim of this talk is to study the classification of expanding algebraic solitons in low dimensions and use these results to check that the Generalized Alekseevskii conjecture holds in these dimensions. This is a joint work with Ramiro Lafuente.