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 : mn 1 → e n+1 1 , isometrically immersed into the lorentz-minkowski space e n+1 1 , is said to be biconservative if the tangent component of vector field ∆2x on mn 1 is identically zero. in this paper, we study the lk-extension of biconservativity condition. the map lk on a hypersurface (as the kth extension of laplace operator l0 = ∆) 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 e n+1 1 , with at most two distinct principal curvatures and some additional conditions, is isoparametric.