Nonnegative sectional curvature hypersurfaces in a real space form

In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form Mn+1(c). We obtain some rigidity results of nonnegative sectional curvature hypersurfaces Mn+1(c) with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product Sk(a) × Sn-k(√1 − a2), 1 ≤ k ≤ n − 1, in Sn+1(1) and the Riemannian product Hk(tanh2r − 1) × Sn-k(coth2r − 1), 1 ≤ k ≤ n − 1, in Hn+1(−1).