ON A CHARACTERIZATION OF ROUND SPHERES

Title & Authors
ON A CHARACTERIZATION OF ROUND SPHERES
Onat, Leyla;

Abstract
It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $\small{C_1}$, $\small{C_2}$, …, $\small{C_{r}}$ such that (equation omitted)d)
Keywords
higher order mean curvature;umbilical points;Minkowski formula;
Language
English
Cited by
1.
A characterization of totally umbilical hypersurfaces in de Sitter space, Journal of Geometry and Physics, 2004, 51, 1, 34
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