## A characterization of the Clifford torus

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- by Qing-Ming Cheng and Susumu Ishikawa PDF
- Proc. Amer. Math. Soc.
**127**(1999), 819-828 Request permission

## 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

- Qing Ming Cheng,
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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
- 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
- © Copyright 1999 American Mathematical Society
- 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