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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 265 (1981), 485-493
- MSC: Primary 53C05; Secondary 55R10
- DOI: https://doi.org/10.1090/S0002-9947-1981-0610960-4
- MathSciNet review: 610960