Endomorphisms of smooth projective 3-folds with non-negative Kodaira dimension

Let X be a nonsingular projective 3-fold with non-negative Kodaira dimension kappa(X) greater than or equal to 0 which admits a nonisomorphic surjective morphism f : X --> X onto itself. If kappa(X) = 0 or 2, a suitable finite etale covering (X) over tilde of X is isomorphic to an abelian 3-fold or the direct product E x S of an elliptic curve E and a nonsingular algebraic surface S with kappa(S) = kappa(X).