A Characterization of Cylinders and an Estimate for Mean Curvature of Convex Euclidean Hypersurfaces Satisfying a Cylindrical Condition

Year 2019, Volume: 12 Issue: 1, 57 - 60, 27.03.2019

Leonard M. Giugiuc Bogdan D. Suceava

https://doi.org/10.36890/iejg.545755

Abstract

We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a

convex smooth hypersurface lying in the four dimensional Euclidean space yields a lower bound

for the mean curvature. The curvature condition we investigate is suggested by the local geometry

of cylinders in the four dimensional Euclidean space.

Keywords

principal curvatures, mean curvature, scalar curvature, Gauss-Kronecker curvature, smooth hypersurfaces

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