  Let X be a compact connected Kaehler manifold such that the holomorphic
tangent bundle TX is numerically effective. A theorem of Demailly, Peternell
and Schenider says that there is a finite unramified Galois covering M --> X, a
complex torus T, and a holomorphic surjective submersion f: M --> T, such that
the fibers of f are Fano manifolds with numerically effective tangent bundle. A
conjecture of Campana and Peternell says that the fibers of f are rational and
homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that
the fibers of f are rational homogeneous varieties. We also prove that the
holomorphic principal G-bundle over T given by f, where G is the group of all
holomorphic automorphisms of a fiber, admits a flat holomorphic connection.
