Half-flat structures on products of three-dimensional Lie groups

2009/12/17 by Fabian Schulte-Hengesbach · 4 citations
Mathematics · #Advanced Algebra and Geometry #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C15 #msc:53C25 #msc:53C30

paper · pdf · doi:10.1016/j.geomphys.2010.06.012

published as J. Geom. Phys. 60 (2010), pp. 1726-1740 · 19 pages

arxiv created 2009/12/17 · openalex publication_date 2010/06/26 · arxiv updated 2010/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We classify six-dimensional Lie groups which admit a left-invariant half-flat SU(3)-structure and which split in a direct product of three-dimensional factors. Moreover, a complete list of those direct products is obtained which admit a left-invariant half-flat SU(3)-structure such that the three-dimensional factors are orthogonal. Similar classification results are proved for left-invariant half-flat SL(3,R)-structures on direct products with either definite and orthogonal or isotropic factors.

Citations

• Curvatures of left invariant metrics on lie groups
• Homogeneous para-Kähler Einstein manifolds

Cited by

• Half-flat structures on decomposable Lie groups
• Half-flat structures on indecomposable Lie groups
• Half-flat structures inducing Einstein metrics on homogeneous spaces
• Construction of nice nilpotent Lie groups

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• Complete left-invariant affine structures on solvable non-unimodular three-dimensional Lie groups
• Low dimensional Lie groups admitting left invariant flat projective or affine structures
• Universal Deformation Formulae for Three-Dimensional Solvable Lie groups
• Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
• Classification of integrable complex structures on 6-dimensional product Lie algebras