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