We consider heterotic string solutions based on a warped product of a
four-dimensional domain wall and a six-dimensional internal manifold,
preserving two supercharges. The constraints on the internal manifolds with
SU(3) structure are derived. They are found to be generalized half-flat
manifolds with a particular pattern of torsion classes and they include
half-flat manifolds and Strominger's complex non-Kahler manifolds as special
cases. We also verify that previous heterotic compactifications on half-flat
mirror manifolds are based on this class of solutions.Comment: 29 pages, reference added, typos correcte