Hypersurfaces with constant mean curvature in spheres

Authors:
Hilário Alencar and Manfredo do Carmo

Journal:
Proc. Amer. Math. Soc. **120** (1994), 1223-1229

MSC:
Primary 53C42; Secondary 53C20

MathSciNet review:
1172943

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact hypersurface of a sphere with constant mean curvature . We introduce a tensor , related to and to the second fundamental form, and show that if , where is a number depending only on and , then either or . We also characterize all with .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1172943-2

Keywords:
Constant mean curvature,
spheres,
minimal surfaces,
totally umbilic,
tori

Article copyright:
© Copyright 1994
American Mathematical Society