In this talk paper, we consider a physical and mathematical concept, namely the biconservative hypersurfaces. Let ψ ∶ M5 → L6 be a spacelike hypersurface in the Lorentz-Minkowski space L6. By definition, Mm is said to be biconservative if the tangent component of the vector field 2ψ is identically zero. This subject is arisen from a well-known conjecture due to Bang-Yen Chen which claims that the only biharmonic submanifolds in the Euclidean spaces are minimal ones. We consider an extended version of biconservativity condition on spacelike hypersurfaces of 6-dimensional Lorentz-Minkowski space with two or three distinct principal curvatures and constant mean curvature.
