An Extended Biconservativity Condition on Hypersurfaces of the Minkowski Spacetime

Isoparametric hypersurfaces of Lorentz-Minkowski spaces, which has been classified by M.A. Magid in 1985, have motivated some researchers to study biconservative hypersurfaces. A biconservative hypersurface has conservative stress-energy with respect to the bienergy functional. A timelike (Lorentzian) hypersurface x: M1 +En+1, isometrically immersed into the Lorentz-Minkowski space I T', is said to be biconservative if the tangent component of vector field A’x on M is identically zero. In this paper, we study the La-extension of biconservativity condition. The map Lk on a hypersurface (as the kth ex of Laplace operator Lo = A) is the linearized operator arisen from the first variation of (k + 1)th mean curvature of hypersurface. After illustrating some examples, we prove that an Lk-biconservative timlike hypersurface of E1+1, with at most two distinct principal curvatures and some additional conditions, is isoparametric.