On the equivalence of two curvature conditions for Lorentzian hypersurfaces

Let n≥3. We show that semi-symmetry and Ricci-semisymmetry conditions are equivalent for any n-dimensional Lorentzian hypersurface in a Lorentzian space form with nonzero curvature. We also show that these curvature conditions are equivalent for any n-dimensional Lorentzian isoparametric hypersurface in Minkowski space R1n+1, and we construct an example of a Ricci-semisymmetric 5-dimensional Lorentzian hypersurface in R16 which is not semi-symmetric.