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A sphere theorem for odd-dimensional submanifolds of spheres


Author: Theodoros Vlachos
Journal: Proc. Amer. Math. Soc. 130 (2002), 167-173
MSC (2000): Primary 53C40; Secondary 53C20.
DOI: https://doi.org/10.1090/S0002-9939-01-06096-8
Published electronically: May 2, 2001
MathSciNet review: 1855635
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Abstract | References | Similar Articles | Additional Information

Abstract:

We establish a topological sphere theorem from the point of view of submanifold geometry for odd-dimensional submanifolds $M^n$ of a unit sphere. We give examples which show that our result is optimal. Moreover, we note the assumption that the dimension $n$ is odd is essential.


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Additional Information

Theodoros Vlachos
Affiliation: Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
Email: tvlachos@cc.uoi.gr

DOI: https://doi.org/10.1090/S0002-9939-01-06096-8
Keywords: Ricci curvature, mean curvature vector, homology groups
Received by editor(s): March 1, 2000
Received by editor(s) in revised form: May 17, 2000
Published electronically: May 2, 2001
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society

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