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

Authors : Leonard M GİUGİUC, Bogdan D SUCEAVA

Pages : 57-60

Doi:10.36890/iejg.545755

View : 44 | Download : 11

Publication Date : 2019-03-27

Article Type : Research Paper

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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