SPHERE-FOLIATED MINIMAL AND CONSTANT MEAN CURVATURE HYPERSURFACES IN PRODUCT SPACES

Constant mean curvature hypersurfaces foliated by spheres ∗

We ask when a constant mean curvature n-submanifold foliated by spheres in one of the Euclidean, hyperbolic and Lorentz–Minkowski spaces (En+1, Hn+1 or Ln+1), is a hypersurface of revolution. In En+1 and Ln+1 we will assume that the spheres lie in parallel hyperplanes and in the case of hyperbolic space Hn+1, the spheres will be contained in parallel horospheres. Finally, Riemann examples in L3...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

Constant Mean Curvature Hypersurfaces with Constant Δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

Hypersurfaces with constant scalar or mean curvature in a unit sphere

Let M be an n(n ≥ 3)-dimensional complete connected hypersurface in a unit sphere S(1). In this paper, we show that (1) if M has non-zero mean curvature and constant scalar curvature n(n−1)r and two distinct principal curvatures, one of which is simple, then M is isometric to the Riemannian product S( √ 1− c2) × Sn−1(c), c = n−2 nr if r ≥ n−2 n−1 and S ≤ (n−1)n(r−1)+2 n−2 + n−2 n(r−1)+2 . (2) i...