For a given complex n-fold M we present an explicit construction of all
complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For
physical applications we consider the case of M being a Calabi-Yau 2-fold. We
show that for such M, there is a subclass of the 3-folds that we construct,
which has natural families of non-Kaehler SU(3)-structures satisfying the
conditions for N = 1 supersymmetry in the heterotic string theory compactified
on the 3-folds. We present examples in the aforementioned subclass with M being
a K3-surface and a 4-torus.Comment: LaTeX, 17 pages, organization of the paper was changed, typos
correcte
