  The Oeljeklaus-Toma (OT-) manifolds are compact, complex, non-Kahler
manifolds constructed by Oeljeklaus and Toma, and generalizing the Inoue
surfaces. Their construction uses the number-theoretic data: a number field $K$
and a torsion-free subgroup $U$ in the group of units of the ring of integers
of $K$, with rank of $U$ equal to the number of real embeddings of $K$. We
prove that any complex subvariety of smallest possible positive dimension in an
OT-manifold is also flat affine. This is used to show that if all non-trivial
elements in $U$ are primitive in $K$, then $X$ contains no proper complex
subvarieties.
