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Cocalibrated structures on Lie algebras with a codimension one Abelian ideal (1109.4774v2)

Published 22 Sep 2011 in math.DG

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.

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