Conformally flat Willmore spacelike hypersurfaces in R n+1

Abstract

In this paper, we give the equation satisfied by umbilics-free Willmore spacelike hypersurfaces using theconformal invariants in Lorentzian space forms. At the same time, we give the equation satisfied by hyperelasticspacelike curves in 2-dimensional Lorentzian space forms and classify the closed hyperelastic spacelike curves. Finallyconformally flat Willmore spacelike hypersurfaces are classified in terms of the hyperelastic spacelike curves in 2-dimensional Lorentzian space forms.