On complete spacelike hypersurfaces with two distinct principal curvatures in Lorentz–Minkowski space

Abstract

We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant m th mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski ( n + 1 ) -spaces ( n ≥ 3 ) of nonzero constant m th mean curvature ( m ≤ n − 1 ) with two distinct principal curvatures λ and μ satisfying inf ( λ − μ ) 2 > 0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder H n − 1 ( c ) × R in terms of square length of the second fundamental form.