Constant mean curvature hypersurfaces foliated by spheres

✍ Scribed by Rafael López

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 138 KB
• Volume: 11
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(99)00037-6

✦ Synopsis

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 hyperbolic space H n+1 , the spheres will be contained in parallel horospheres. Finally, Riemann examples in L 3 are constructed, that is, non-rotational spacelike surfaces foliated by circles in parallel planes.