A+ CATEGORY SCIENTIFIC UNIT

A new characterization of the sphere in $R^3$

Volume 38 / 1980

Thomas Hasanis Annales Polonici Mathematici 38 (1980), 47-49 DOI: 10.4064/ap-38-1-47-49

Abstract

Let M be a closed connected surface in $R^3$ with positive Gaussian curvature K and let $K_II$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_II = c√HK^r$, for some constants c and r, where H is the mean curvature of M.

Authors

  • Thomas Hasanis

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