Balanced metrics on non-Kähler Calabi-Yau threefolds

Abstract

We construct balanced metrics on the family of non-Kähler Calabi-Yau threefolds that are obtained by smoothing after contracting $(−1,−1)$-rational curves on a Kähler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to the connected sum of $k \ge 2$ copies of $S^3 × S^3$.