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

https://izlik.org/JA56WA77DE

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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