Nonnegative sectional curvature hypersurfaces in a real space form

In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form M n+1(c). We obtain some rigidity results of nonnegative sectional curvature hypersurfaces M n+1(c) with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product S k (a) × S n-k (√1 − a 2), 1 ≤ k ≤ n − 1, in S n+1(1) and the Riemannian product H k (tanh2 r − 1) × S n-k (coth2 r − 1), 1 ≤ k ≤ n − 1, in H n+1(−1).