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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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
Keywords
- Cocalibrated structures
- Lie algebras with codimension one Abelian ideals
- Special geometry on Lie algebras