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