Geodesic
Sphere theorem by means of the ratio of meancurvature functions
Glasgow mathematical journal, Tome 42 (2000) no. 1, pp. 91-95

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It is wellknown that a compact embedded hypersurface of the Euclidean space withoutboundary is a round sphere if one of mean curvature functions is constant. Inthis note, we show that a compact embedded hypersurface of the Euclidean space(and other constant curvature spaces) without boundary is a round sphere if theratio of some two mean curvature functions isconstant.1991 Mathematics Subject Classification 53C40, 53C20. 
Koh, Sung-Eun. Sphere theorem by means of the ratio of meancurvature functions. Glasgow mathematical journal, Tome 42 (2000) no. 1, pp. 91-95. doi: 10.1017/S0017089500010119
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