Publ. Math. Debrecen 58 / 4 (2001), 587–604 On some class of hypersurfaces of semi-Euclidean spaces By CENGIZHAN MURATHAN (Bursa), KADRI ARSLAN (Bursa), RYSZARD DESZCZ (Wroclaw), RIDVAN EZENTAS . (Bursa) and CIHAN ¨ OZG ¨ UR (Bursa) Dedicated to the 60th birthday of Professor Dr. Hilmi H. Hacisalihoˇ glu Abstract. In the paper we prove that under some additional curvature condition the relations R · R = 0 and R · S = 0 are equivalent for hypersurfaces of semi-Euclidean spaces. We present also examples of hypersurfaces having the curvature tensor expressed by the square, in the sense of the Kulkarni–Nomizu product, of the Ricci tensor. 1. Introduction Let (M,g), n = dim M ≥ 3, be a connected semi-Riemannian man- ifold of class C ∞ and let ∇ be its Levi–Civita connection. A manifold (M,g) is said to be semisymmetric ([26]) if (1) R · R =0 on M . Every locally symmetric manifold (∇R = 0) is semisymmetric. The converse statement is not true. For precise definitions of the symbols used, Mathematics Subject Classification : 53B20, 53B25, 53B50. Key words and phrases : pseudosymmetry type manifold, Ricci-semisymmetric mani- fold, semisymmetric manifold, hypersurface. The third named author is supported by the Polish State Committee of Scientific Re- search (KBN) and the Uludaˇg University in Bursa, Turkey, during his visit to this University.