  The Oeljeklaus-Toma (OT-) manifolds are complex manifolds constructed by
Oeljeklaus and Toma from certain number fields, and generalizing the Inoue
surfaces $S_m$. On each OT-manifold we construct a holomorphic line bundle with
semipositive curvature form and trivial Chern class. Using this form, we prove
that the OT-manifolds admitting a locally conformally Kahler structure have no
non-trivial complex subvarieties. The proof is based on the Strong
Approximation theorem for number fields, which implies that any leaf of the
null-foliation of w is Zariski dense.
