  In this paper we aim at the description of foliations having tangent sheaf
$T\mathcal F$ with $c_1(T\mathcal F)=c_2(T\mathcal F)=0$ on non-uniruled
projective manifolds. We prove that the universal covering of the ambient
manifold splits as a product, and that the Zariski closure of a general leaf of
$\mathcal F$ is an Abelian variety. It turns out that the analytic type of the
Zariski closures of leaves may vary from leaf to leaf. We discuss how this
variation is related to arithmetic properties of the tangent sheaf of the
foliation.
