Sharif Digital Repository

All known examples of homogeneous Einstein spaces with negative scalar curvature (non compact) are isometric to standard Einstein solvmanifolds . we prove that any nilpotent Lie algebra having a codimension-one abelian ideal is the nilradical of a rank –one Einstein solvmanifold . In other words this nilpotent Lie algebra admits a rank-one solvable extension which can be endowed with an Einstein left invariant Riemannian metric . also a curve of pairwise non-isometric 8-dimensional rank-one Einstein solvmanifold is given .