SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN SPHERES

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

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 Scalar Curvature

Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M must be the sphere. On the other hand, when the curvature of M is zero, a theorem of Har tman-Nirenberg [4] says that M must be a plane or a cylinder. These two theorems complete the classification of com...

hypersurfaces with constant mean curvature in a lorentzian space form

Rigidity of minimal hypersurfaces of spheres with constant ricci curvature

ABSTRACT: Let M be a compact oriented minimal hypersurface of the unit n-dimensional sphere S. In this paper we will point out that if the Ricci curvature of M is constant, then, we have that either Ric ≡ 1 andM is isometric to an equator or, n is odd,Ric ≡ n−3 n−2 andM is isometric to S n−1 2 ( √ 2 2 )×S n−1 2 ( √ 2 2 ). Next, we will prove that there exists a positive number ̄(n) such that if ...