Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
arXiv:1109.4774
Abstract
Cocalibrated G_2-structures and cocalibrated G_2^*-structures are the natural initial values for Hitchin's evolution equations whose solutions define (pseudo)-Riemannian manifolds with holonomy group contained in Spin(7) or Spin_0(3,4), respectively. In this article, we classify which seven-dimensional real Lie algebras with a codimension one Abelian ideal admit such structures. Moreover, we classify the seven-dimensional complex Lie algebras with a codimension one Abelian ideal which admit cocalibrated (G_2)_C-structures.
18 pages, v2: typos corrected