Abstract
There are many research papers for isoparametric hypersurfaces in Riemannian space forms and almost perfect results have already been got till now. In the late 20th century, the Lorentzian isoparametric hypersurfaces in the Lorentzian space $\bbr_1^{n+1}$ and the Lorentzian hyperbolic space $H_1^{n+1}$ have been completely classified. Continuing with our previous work, we investigate Lorentzian isoparametric hypersurfaces in the Lorentzian sphere $S_1^{n+1}$ in this paper.Then complete classification and analytic expression are given for all kinds of Lorentzian isoparametric hypersurfaces in $S_1^{n+1}$.
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