On the ‘standard’ condition for noncompact homogeneous Einstein spaces. Geom. Dedicata 105 (2004), 77–83

Abstract. A nonflat Einstein solvmanifold (S, g) is said to be of standard type if in the associated metric Lie algebra s, the orthogonal complement a of the derived algebra is abelian. It is an open question whether the standard condition is automatically satisfied for all nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra s of a nonflat Einstein solvmanifold (S, g) under the assumption dim[a, a] ≤ 1. In particular, we obtain some new sufficient conditions which imply standard type. 1