Minimal hypersurfaces in an $m$-sphere
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- by Bang-yen Chen PDF
- Proc. Amer. Math. Soc. 29 (1971), 375-380 Request permission
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.References
- Bang-yen Chen, On a theorem of Fenchel-Borsuk-Willmore-Chern-Lashof, Math. Ann. 194 (1971), 19β26. MR 291994, DOI 10.1007/BF01351818
- Takehiro Itoh, Complete surfaces in $E^{4}$ with constant mean curvature, K\B{o}dai Math. Sem. Rep. 22 (1970), 150β158. MR 267496
- H. Blaine Lawson Jr., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. (2) 89 (1969), 187β197. MR 238229, DOI 10.2307/1970816
- Robert Osserman, Minimal varieties, Bull. Amer. Math. Soc. 75 (1969), 1092β1120. MR 276875, DOI 10.1090/S0002-9904-1969-12357-8
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 375-380
- MSC: Primary 53.04
- DOI: https://doi.org/10.1090/S0002-9939-1971-0285999-0
- MathSciNet review: 0285999