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Annali di Matematica Pura ed Applicata

, Volume 58, Issue 1, pp 303–315 | Cite as

A characteristic property of spheres

  • A. D. Alexandrov
Article

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\({}_{\partial \xi _i }^{\partial \varphi } > 0\). Then if φ(k1, ..., kn)=const on S and S is subject to some additional general conditions (those(II0) or(II) no 1), S is a sphere.

Keywords

General Condition Characteristic Property Constant Curvature Principle Curvature Additional General Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Nicola Zanichelli Editore 1962

Authors and Affiliations

  • A. D. Alexandrov
    • 1
  1. 1.LeningradU. R. S. S.

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