Two characteristic properties of the sphere-Reference-Cited by-同舟云学术

Two characteristic properties of the sphere

Published:1974 Issue:1 Volume:44 Page:176-178
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Koutroufiotis Dimitri

Abstract

Let S S be a closed, convex surface in E 3 {E^3} with positive Gaussian curvature K K and let K II {K_{{\text {II}}}} be the curvature of its second fundamental form. It is shown that S S is a sphere if K II ≡ c K {K_{{\text {II}}}} \equiv cK for some constant c c or if K II ≡ √ K {K_{{\text {II}}}} \equiv \surd K .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-044-01/S0002-9939-1974-0339025-8/S0002-9939-1974-0339025-8.pdf

Reference1 articles.

1. Closed convex hypersurfaces with second fundamental form of constant curvature;Schneider, Rolf;Proc. Amer. Math. Soc.,1972

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