Closed G2-structures with negative Ricci curvature

We study existence problems for closed G(2)-structures with negative Ricci curvature, and we prove the G(2)-Goldberg conjecture for noncompact manifolds. We first show that no closed manifold admits a closed G(2)-structure with negative Ricci curvature. In the noncompact setting, we show that no complete manifold admits a closed G(2)-structure with Ricci curvature pinched sufficiently close to a negative constant. As a consequence, an Einstein closed G(2)-structure on a complete manifold must be torsion-free. In addition, when the Einstein metric is incomplete, we find restrictions on lengths of geodesics.