Para-Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms

Let x : Mⁿ → M₁ⁿ⁺¹(c) be an umbilic-free spacelike hypersurface in the (n+ 1)-dimensional Lorentzian space form M₁ⁿ⁺¹(c). Three basic conformal invariants of Mⁿ are the conformal 1-form C, the conformal second fundamental form B, and the Blaschke tensor A. The para-Blaschke tensor D^λ = A + λB which is a linear combination of A and B for some constant λ is a symmetric (0, 2)-tensor. A spacelike hypersurface is called a para-Blaschke isoparametric spacelike hypersurface if the conformal 1-form vanishes and the eigenvalues of the para-Blaschke tensor are constant. In this paper, we classify the para-Blaschke isoparametric spacelike hypersurfaces under the conformal group of M₁ⁿ⁺¹(c).