Archiv der Mathematik | 2021
Existence of left invariant Ricci flat metrics on nilpotent Lie groups
Abstract
In this paper, we study the problem of the existence of left invariant Ricci flat metrics on nilpotent Lie groups. We mainly prove that any nilpotent Lie algebra obtained by a double extension of an Abelian Lie algebra admits at least one left invariant Ricci flat metric. As an application, we obtain certain new nilpotent Lie algebras which admit left invariant Ricci flat metrics.