2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99859We find sufficient conditions for a principal toric bundle over compact Kähler manifolds to admit Calabi-Yau connections with torsion. With the aids of a topological classification, we construct such geometry on $n(S^2\times S^4)#(n+1)(S^3\times S^3)$18 pages, final version to appear in J.Diff.GeomDifferential GeometryHigh Energy Physics - Theory53C55text