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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal hypersurfaces in an $ m$-sphere


Author: Bang-yen Chen
Journal: Proc. Amer. Math. Soc. 29 (1971), 375-380
MSC: Primary 53.04
MathSciNet review: 0285999
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Abstract: (1) A submanifold $ {M^n}$ of a euclidean space $ {E^{n + 2}}$ of codimension 2 is a pseudo-umbilical submanifold with constant mean curvature if and only if it is a minimal hypersurface of a hypersphere of $ {E^{n + 2}}$. (2) A complete oriented minimal surface $ {M^2}$ of a 3-sphere $ {S^3}$ on which the Gauss curvature does not change its sign is either an equatorial sphere or a Clifford flat torus.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0285999-0
PII: S 0002-9939(1971)0285999-0
Keywords: Second fundamental form, mean curvature vector, mean curvature, pseudo-umbilical submanifold, minimal hypersurface, equatorial sphere, Clifford flat torus, Gauss curvature
Article copyright: © Copyright 1971 American Mathematical Society