Geodesic
Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions
Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 275-276

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It is shown that an immersion of n dimensional compact oriented manifold without boundary into the n+1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilic immersion if one of the mean curvature function H_l does not vanish and the ratio H_k/H_l is constant, 1\leq k, l \leq n, k\ne l. 
Koh, Sung-Eun; Lee, Seung-Won. Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions. Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 275-276. doi: 10.1017/S0017089501020110
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     title = {Addendum to the paper: {Sphere} theorem by means of the ratio of mean curvature functions},
     journal = {Glasgow mathematical journal},
     pages = {275--276},
     year = {2001},
     volume = {43},
     number = {2},
     doi = {10.1017/S0017089501020110},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501020110/}
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