  Let $Y$ be a compact complex manifold embedded in a complex manifold with
unitary flat normal bundle. Our interest is in a sort of the linearizability
problem of a neighborhood of $Y$. As a higher-codimensional generalization of
Ueda's result, we give a sufficient condition for the existence of a
non-singular holomorphic foliation on a neighborhood of $Y$ which includes $Y$
as a leaf with unitary-linear holonomy. We apply this result to the existence
problem of a smooth Hermitian metric with semi-positive curvature on a nef line
bundle.
