Resumen de Closed 2G2-eigenforms and exact 2G2-structures

Marco Freibert, Simon Salamon

• 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