Unflat connections in $3$-sphere bundles over $S\sp{4}$

Andrzej Derdzi{ński, A. Rigas
1981 Transactions of the American Mathematical Society  
The paper concerns connections in 3-sphere bundles over 4-manifolds having the property of unflatness, which is a necessary condition in order that a natural construction give a Riemannian metric of positive sectional curvature in the total space. It is shown that, as conjectured by A. Weinstein, the only 3-sphere bundle over S4 with an unflat connection is the Hopf bundle.
doi:10.1090/s0002-9947-1981-0610960-4 fatcat:7zb26esi6bd6rerfyxnkunqhxa