Fibered Calabi-Yau threefolds with relative automorphisms of positive entropy and $c_2$-contractions

We show that an abelian fibered Calabi-Yau threefold with a positive entropy automorphism preserving the fibration is unique up to isomorphisms as fibered varieties. We also give a fairly explicit structure theorem of an elliptically fibered Calabi-Yau threefold with a positive entropy automorphism preserving the fibration.