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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on sphere-type theorems


Authors: Hyeong In Choi, Sang Moon Kim and Sung Ho Park
Journal: Proc. Amer. Math. Soc. 125 (1997), 569-572
MSC (1991): Primary 53C20
MathSciNet review: 1343684
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Abstract: We prove if $M$ is a complete Riemannian manifold with an embedded totally geodesic compact hypersurface $N$ such that $M$ has nonnegative sectional curvature, and the sectional curvature of $M$ is strictly positive in a neighborhood of $N$, then the pair $(M,N)$ is diffeomorphic to the pair $(S^n,S^{n-1})/\pi _1(M)$. This result gives an affirmative answer to a question of H. Wu in the case when $M$ is compact and simply connected.


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Additional Information

Hyeong In Choi
Affiliation: Department of Mathematics, Seoul National University, Seoul, 151-742 Korea
Email: hichoi@math.snu.ac.kr

Sang Moon Kim
Affiliation: Department of Mathematics, Seoul National University, Seoul, 151-742 Korea

Sung Ho Park
Affiliation: Department of Mathematics, Seoul National University, Seoul, 151-742 Korea

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03480-1
PII: S 0002-9939(97)03480-1
Keywords: Sphere theorem, Morse theory, convex function
Received by editor(s): May 22, 1995
Additional Notes: Supported in part by BSRI-94-1416, and by GARC
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society