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

We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant mmth 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)(n+1)-spaces (n≥3n≥3) of nonzero constant mmth mean curvature (m≤n−1m≤n−1) with two distinct principal curvatures λλ and μμ satisfying inf(λ−μ)2>0inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hn−1(c)×RHn−1(c)×R in terms of square length of the second fundamental form.