On SO(3)-bundles over the Wolf spaces

Abstract

We study the formality of the total space of principal SU(2) and SO(3)bundles over a Wolf space, that is a symmetric positive quaternionic K¨ahler manifold. We apply this to conclude that all the 3-Sasakian homogeneous spaces are formal. We also determine the principal SU(2) and SO(3)-bundles over the Wolf spaces whose total space is non-formal.