Constant mean curvature hypersurfaces foliated by spheres

Abstract

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.