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Hypersurfaces with constant scalar curvature and constant mean curvature

โœ Scribed by Thomas Hasanis; Theodoros Vlachos

Publisher
Springer
Year
1995
Tongue
English
Weight
394 KB
Volume
13
Category
Article
ISSN
0232-704X

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We ask when a constant mean curvature n-submanifold foliated by spheres in one of the Euclidean, hyperbolic and Lorentz-Minkowski spaces (E n+1 , H n+1 or L n+1 ), is a hypersurface of revolution. In E n+1 and L n+1 we will assume that the spheres lie in parallel hyperplanes and in the case of hyper

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In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced