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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Andrzej Derdziński and A. Rigas
Journal: Trans. Amer. Math. Soc. 265 (1981), 485-493
MSC: Primary 53C05; Secondary 55R10
MathSciNet review: 610960
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0610960-4
PII: S 0002-9947(1981)0610960-4
Keywords: Unflat connection, positive sectional curvature, $ 3$-sphere bundle
Article copyright: © Copyright 1981 American Mathematical Society