On fibrations with formal elliptic fibers

We prove that for a fibration of simply-connected spaces of finite type $F\hookrightarrow E\to B$ with $F$ being positively elliptic and $H^*(F,\qq)$ not possessing non-trivial derivations of negative degree, the base $B$ is formal if and only if the total space $E$ 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.

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