Clasificación de nilradicales Einstein filiformes de dimension 8

ROMINA M. ARROYO

Mendoza, Argentina

Congreso; Reunión Anual de la Unión Matemática Argentina; 2008

Unión Matemática Argentina

A Riemannian manifold (M,g) is said to be Einstein if its Ricci tensor satisfies ric(g)=cg, for some c. In the homogeneous case, a problem that is still open is the so called Alekseevskii Conjecture. This conjecture says that any homogeneous Einstein space with negative scalar curvature (i.e. c<0) is a solvmanifold: a simply connected solvable Lie group endowed with a left invariant Riemannian metric. The aim of this paper is to classify Einstein solvmanifolds of dimension 9 whose nilradicals are filiform (i.e. (n-1)-step nilpotent and n-dimensional).