on biconservative riemannian hypersurfaces of lorentzian 4-space forms

In this manuscript, we consider an extended version of bi-conservativity condition (namely, c-biconservativity) on the riemannian hypersurfaces of lorentzian standard 4-space forms. this new condi-tion is obtained by substituting the cheng-yau operator c instead of the laplace operator ∆. we show that every c-biconservative riemannian hypersurface of a lorentzian 4-space form with constant mean curvature has constant scalar curvature.