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1997•Proceedings of the American Mathematical SocietyOpen access

Hypersurfaces in a sphere with constant mean curvature

Zhong Hua Hou

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Abstract

Let M n M^n be a closed hypersurface of constant mean curvature immersed in the unit sphere S n + 1 S^{n+1} . Denote by S S the square of the length of its second fundamental form. If S > 2 n − 1 S>2\sqrt {n-1} , M M is a small hypersphere in S n + 1 S^{n+1} . We also characterize all M n M^n with S = 2 n − 1 S=2\sqrt {n-1} .

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Let M n M^n be a closed hypersurface of constant mean curvature immersed in the unit sphere S n + 1 S^{n+1} . Denote by S S the square of the length of its second fundamental form. If S > 2 n − 1 S>2\sqrt {n-1} , M M is a small hypersphere in S n + 1 S^{n+1} . We also characterize all M n M^n with S = 2 n − 1 S=2\sqrt {n-1} .

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Available abstract

Let M n M^n be a closed hypersurface of constant mean curvature immersed in the unit sphere S n + 1 S^{n+1} . Denote by S S the square of the length of its second fundamental form. If S > 2 n − 1 S>2\sqrt {n-1} , M M is a small hypersphere in S n + 1 S^{n+1} . We also characterize all M n M^n with S = 2 n − 1 S=2\sqrt {n-1} .

Key concepts: Constant (computer programming), Mean curvature, Curvature, Center of curvature, Constant curvature, Mathematics, Geometry, Mathematical analysis

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