A construction of non-Kähler Calabi-Yau manifolds and new solutions to the Strominger system

We propose a new construction of compact non-Kähler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on Σg×T4, where Σg is an immersed minimal surface of genus g≥3 in flat T3.