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A characterization of the Clifford torus


Authors: Qing-Ming Cheng and Susumu Ishikawa
Journal: Proc. Amer. Math. Soc. 127 (1999), 819-828
MSC (1991): Primary 53C20, 53C42
DOI: https://doi.org/10.1090/S0002-9939-99-05088-1
MathSciNet review: 1636934
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Abstract: In this paper, we prove that an $n$-dimensional closed minimal hypersurface $M$ with Ricci curvature $Ric(M) \geq \dfrac{n}{2}$ of a unit sphere $S^{n+1}(1)$ is isometric to a Clifford torus if $n\leq S\leq n+\frac{14(n+4)}{9n+30}$, where $S$ is the squared norm of the second fundamental form of $M$.


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

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Additional Information

Qing-Ming Cheng
Affiliation: Department of Mathematics, Faculty of Science, Josai University, Sakado, Saitama 350-0295, Japan
Email: cheng@math.josai.ac.jp

Susumu Ishikawa
Affiliation: Department of Mathematics, Saga University, Saga 840-0027, Japan

DOI: https://doi.org/10.1090/S0002-9939-99-05088-1
Keywords: Minimal hypersurfaces, scalar curvature, Ricci curvature, Clifford torus
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: November 1, 1996
Additional Notes: The first author’s research was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture and by a Grant-in-Aid for Scientific Research from Josai University.
The second author’s research was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture.
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

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