Constant mean curvature spheres in homogeneous three-manifolds
Constant mean curvature spheres in homogeneous three-manifolds
Abstract We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional …