We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with respect to the Chern connection.
"Non-nilpotent complex geometry of nilmanifolds and heterotic supersymmetry." Asian J. Math. 18 (2) 229 - 246, April 2014.