A characteristic property of spheres |
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Authors: | A D Alexandrov |
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Affiliation: | (1) Leningrad, U. R. S. S. |
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Abstract: | Summary We prove: Let S be a closed n-dimensional surface in an(n+1)-space of constant curvature (n ≥ 2); k1 ≥ ... ≥ kn denote its principle curvatures. Let φ(ξ1, ..., ξn) be such that
. Then if φ(k1, ..., kn)=const on S and S is subject to some additional general conditions (those(II
0) or(II) no 1), S is a sphere.
To Enrico Bompiani on his scientific Jubilee |
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Keywords: | |
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