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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Open nonnegatively curved $ 3$-manifolds with a point of positive curvature


Author: Doug Elerath
Journal: Proc. Amer. Math. Soc. 75 (1979), 92-94
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1979-0529221-3
MathSciNet review: 529221
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Abstract: Let M be a complete open nonnegatively curved Riemannian 3-manifold with a point at which all sectional curvatures are positive, and suppose that M contains a pole. Then M is not flat on the complement of any compact set. Note that this is clearly false for 2-manifolds.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0529221-3
Article copyright: © Copyright 1979 American Mathematical Society