Nilmanifolds with a calibrated G_2 structure

We introduce obstructions to the existence of a calibrated G2-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G2-structure. © 2011 Elsevier B.V.