Closed 2G2-eigenforms and exact 2G2-structures
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Marco Freibert [1] ; Simon Salamon [2]
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[1] Kiel University
Kiel University
Kreisfreie Stadt Kiel, Alemania
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[2] King's College London
King's College London
Reino Unido
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 6, 2022, págs. 1827-1866
- Idioma: inglés
- DOI: 10.4171/RMI/1315
- Enlaces
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Resumen
A study is made of left-invariant G2G2-structures with an exact 3-form on a Lie group G whose Lie algebra g admits a codimension-one nilpotent ideal ℎh. It is shown that such a Lie group G cannot admit a left-invariant closed G2G2-eigenform for the Laplacian and that any compact solvmanifold Γ\G arising from G does not admit an (invariant) exact G2G2-structure. We also classify the seven-dimensional Lie algebras g with codimension-one ideal equal to the complex Heisenberg Lie algebra which admit exact G2G2-structures with or without special torsion. To achieve these goals, we first determine the six-dimensional nilpotent Lie algebras ℎh admitting an exact SL(3,C)-structure ρ or a half-flat SU(3)SU(3)-structure (ω,ρ) with exact ρ, respectively
