The Alekseevskii conjecture: Overview and open questions

LAFUENTE, RAMIRO A.; ARROYO, ROMINA M.

Congreso; Annual meeting of the Australian Mathematical Society; 2018

One of the most important open problems on Einstein homogeneous manifolds is theAlekseevskii conjecture. This conjecture says that any connected homogeneous Einstein space of negative scalar curvature is diFFeomorphic to a Euclidean space.In this talk we aim to discuss recent advances towards the above mentioned conjecture, share our contributions and describe some open problems.This talk is based in a joint work with Ramiro Lafuente (The University of Queens-land).