Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces


Marta Dabrowska, Filip Defever, Ryszard Deszcz, Dorota Kowalczyk


In the context of P.J. Ryan's problem on the equivalence of the conditions $R \cdot R = 0$ and $R \cdot S = 0$ for hypersurfaces, we prove that there is indeed equivalence for hypersurfaces of semi-Euclidean spaces in any dimension, under an additional curvature condition of semisymmetric type.