On fibrations with formal elliptic fibers

We prove that for a fibration of simply-connected spaces of finite type F↪E→B with FF being positively elliptic and H∗(F,Q)H∗(F,Q) not possessing non-trivial derivations of negative degree, the base BB is formal if and only if the total space EE is formal. Moreover, in this case the fibration map is a formal map. As a geometric application we show that positive quaternion Kähler manifolds are formal and so are their associated twistor fibration maps.