Geodesic
Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces
Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 103 .

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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.
Classification : 53B20 53B30 
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     author = {Marta Dabrowska and Filip Defever and Ryszard Deszcz and Dorota Kowalczyk},
     title = {Semisymmetry and {Ricci-symmetry} for {Hypersurfaces} of {Semi-euclidean} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {103 },
     publisher = {mathdoc},
     volume = {_N_S_67},
     number = {81},
     year = {2000},
     zbl = {0951.53015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a9/}
}
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Marta Dabrowska; Filip Defever; Ryszard Deszcz; Dorota Kowalczyk. Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces. Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 103 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a9/