A global pinching theorem for surfaces with constant mean curvature in

Authors:
Yi-Jung Hsu and Tai-Ho Wang

Journal:
Proc. Amer. Math. Soc. **130** (2002), 157-161

MSC (2000):
Primary 53C40, 53C42

DOI:
https://doi.org/10.1090/S0002-9939-01-06030-0

Published electronically:
May 3, 2001

MathSciNet review:
1855633

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let be a compact immersed surface in the unit sphere with constant mean curvature . Denote by the linear map from into , , where is the linear map associated to the second fundamental form and is the identity map. Let denote the square of the length of . We prove that if , then is either totally umbilical or an -torus, where is a constant depending only on the mean curvature .

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Additional Information

**Yi-Jung Hsu**

Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

Email:
yjhsu@math.nctu.edu.tw

**Tai-Ho Wang**

Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

Email:
teich@math.sinica.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-01-06030-0

Keywords:
Mean curvature,
sphere,
totally umbilical

Received by editor(s):
April 17, 1997

Received by editor(s) in revised form:
May 10, 2000

Published electronically:
May 3, 2001

Communicated by:
Christopher Croke

Article copyright:
© Copyright 2001
American Mathematical Society