Abstract
In this paper we consider closed SL(3,C)-structures which are either mean convex or tamed by a symplectic form. These notions were introduced by Donaldson in relation to G2-manifolds with boundary. In particular, we classify nilmanifolds which carry an invariant mean convex closed SL(3,C)-structure and those which admit an invariant mean convex half-flat SU(3)-structure. We also prove that, if a solvmanifold admits an invariant tamed closed SL(3,C)-structure, then it also has an invariant symplectic half-flat SU(3)-structure.
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