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.
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