Open nonnegatively curved $3$-manifolds with a point of positive curvature
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- by Doug Elerath PDF
- Proc. Amer. Math. Soc. 75 (1979), 92-94 Request permission
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
- Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. MR 309010, DOI 10.2307/1970819
- Detlef Gromoll and Wolfgang Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90. MR 247590, DOI 10.2307/1970682
- Walter A. Poor Jr., Some results on nonnegatively curved manifolds, J. Differential Geometry 9 (1974), 583–600. MR 375155
Additional Information
- © Copyright 1979 American Mathematical Society
- 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