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Proceedings of the American Mathematical Society

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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.


References [Enhancements On Off] (What's this?)

  • [1] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413-443. MR 0309010 (46:8121)
  • [2] D. Gromoll and W. Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75-90. MR 0247590 (40:854)
  • [3] W. A. Poor, Some results on nonnegatively curved manifolds, J. Differential Geometry 9 (1974), 583-600. MR 0375155 (51:11351)

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

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