Hypersurfaces with Constant Squared Norm of Second Fundamental Form

Abstract

Let M n be an n(n 3)-dimensional complete connected and oriented hypersurface with constant squared norm of the second fundamental form and two distinct principal curvatures in a real space form M n+1 (c). Denote by S k (a) the k-dimensional sphere with radius a, where a is a constant parameter, we obtain some nonexistence theorems and some characterizations of the Riemannian products: R k S n−k (a), or S k (a) S n−k ( p 1 a2), or S k (a) H n−k ( p 1 + a2) in M n+1 (c)(c = 0;1; 1), where 1 < k n 1.