on 1-maximal hypersurfaces in lorentzian hyperbolic 5-space

In this paper, we talk about the 1-maximal hypersurfaces in the standard lorentzian hyperbolic space h5 1 with sectional curvature -1. let m4 be a riemannian hypersurface of h5 1 isometrically immersed by the position map x : m4 ! h5 1. the hypersurface m4 is called 1-maximal if its second mean curvature is identically zero. we assume that the position map x satisfies the c-biharmonicity condition c2x = 0, where c is the cheng-yau operator. we show that if a c-biharmonic hypersurface m4 has at most two distinct principal and constant mean curvature, then it has to be 1-maximal.