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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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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