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Cocalibrated structures on Lie algebras with a codimension one Abelian ideal

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Abstract

Cocalibrated G2-structures and cocalibrated \({{\rm G}_2^*}\)-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 Spin0(3, 4), respectively. In this article, we classify 7-D real Lie algebras with a codimension one Abelian ideal which admit such structures. Moreover, we classify the 7-D complex Lie algebras with a codimension one Abelian ideal which admit cocalibrated \({({\rm G}_2)_{\mathbb{C}}}\)-structures.

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  1. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, Hamburg, 20146, Germany

    Marco Freibert

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  1. Marco Freibert
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Correspondence to Marco Freibert.

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Freibert, M. Cocalibrated structures on Lie algebras with a codimension one Abelian ideal. Ann Glob Anal Geom 42, 537–563 (2012). https://doi.org/10.1007/s10455-012-9326-0

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  • DOI: https://doi.org/10.1007/s10455-012-9326-0

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