We construct explicit compact solutions with non-zero field strength,
non-flat instanton and constant dilaton to the heterotic string equations in
dimensions seven and eight. We present a quadratic condition on the curvature
which is necessary and sufficient the heterotic supersymmetry and the anomaly
cancellation to imply the heterotic equations of motion in dimensions seven and
eight. We show that some of our examples are compact supersymmetric solutions
of the heterotic equations of motion in dimensions seven and eight.Comment: LaTeX2e, 25 pages, LaTeX typos correcte
