Cocalibrated structures on Lie algebras with a codimension one Abelian ideal

Details Cocalibrated structures on Lie algebras with a codimension one Abelian ideal Cocalibrated structures on Lie algebras with a codimension one Abelian ideal

2011-09-22

arxiv.org/abs/1109.4774v2

Mathematics

Differential Geometry

18 pages, v2: typos corrected

Scientific paper

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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