In this talk paper, we consider an advanced version of a well-known conjecture introduced by Bang-Yen Chen in 1980’s. The mentioned conjecture claims that the only biharmonic submanifolds in the Euclidean spaces are minimal ones. We are focused to confirm that claim about some spacelike hypersurfaces of the Lorentz-Minkowski 6-space, L6. We prove the 1-maximality of C-biharmonic spacelike hypersurface of L6 with two or three distinct principal curvatures and constant mean curvature.
