Rotation hypersurfaces in lorentz-minkowski space with constant mean curvature

Abstract

We give explicit parameterizations of rotation hypersurfaces in Lorentz-Minkowski space $L^{n+1}$. Then we obtain rotation hypersurfaces in Lorentz-Minkowski space $L^{n+1}$ with constant mean curvature. In particular, we determine nonplanar rotation hypersurfaces with zero mean curvature, namely, generalized catenoids of $L^{n+1}$. In the case the rotation axis is light-like, the generalized catenoids generalize Enneper's surfaces of the 2nd and 3rd kind.