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 | References | Similar Articles | Additional Information

Abstract: In this paper, we prove that an -dimensional closed minimal hypersurface with Ricci curvature of a unit sphere is isometric to a Clifford torus if , where is the squared norm of the second fundamental form of .

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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