Unflat connections in 3-sphere bundles over 𝑆⁴

Derdziński, Andrzej; Rigas, A.

doi:10.1090/S0002-9947-1981-0610960-4

Unflat connections in $3$-sphere bundles over $S^{4}$
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by Andrzej Derdziński and A. Rigas PDF

Trans. Amer. Math. Soc. 265 (1981), 485-493 Request permission

Abstract:

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 ${S^4}$ with an unflat connection is the Hopf bundle.

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