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1982•Journal of the Australian Mathematical Society Series A Pure Mathematics and StatisticsOpen access

Conformal variation of a hypersurface of constant mean curvature in an einstein space

Geoffrey Howard Smith

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Abstract

Abstract Let a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.

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Abstract Let a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.

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Available abstract

Abstract Let a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.

Key concepts: Hypersurface, Conformal map, Mean curvature, Mathematics, Immersion (mathematics), Einstein, Space form, Mathematical analysis

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