A global pinching theorem of minimal hypersurfaces in the sphere

Author:
Chun Li Shen

Journal:
Proc. Amer. Math. Soc. **105** (1989), 192-198

MSC:
Primary 53C42; Secondary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-1989-0973845-2

MathSciNet review:
973845

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Abstract: Let be a compact embedded minimal hypersurface in the sphere , and the square of the length of the second fundamental form of . Suppose has nonnegative Ricci curvature. Then there is a constant , depending only on , such that if , then must be totally geodesic. Here . It is related to the results of J. Simons [6] and S. T. Yau [9] about the minimal hypersurfaces in the sphere. For the case , we also have a similar discussion.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0973845-2

Article copyright:
© Copyright 1989
American Mathematical Society