Abstract
A semi-Riemannian manifold (M;g), n 3, is called semisymmetricifR R = 0 (1)holds on M: It is well known that the class of semisymmetric mani-folds includes the set of locally symmetric manifolds (rR = 0) as aproper subset. Semisymmetric Riemannian manifolds were –rst stud-ied by E. Cartan, A. Lichnerowicz, R. S. Couty and N. S. Sinjukov. In[34] K. Nomizu asked the question if there exist complete, irreducibleand simply connected, Riemannian manifolds of dimension n 3 sat-isfying (1) and not locally symmetric. The –rst positive example wasconstructed by H. Takagi ([39]). A fundamental study on Riemann-ian semisymmetric manifolds was made by Z. I. Szabo ([36], [37], and[38]) and O. Kowalski (see [6] and the references therein). Semisym-metric semi-Riemannian manifolds, among others, were studied by A.Derdzinski and W. Roter. In particular, they have investigated semi-symmetric manifolds having parallel Weyl tensor (rC = 0) as well assemisymmetric manifolds with recurrent Weyl tensor (rC = C ). A
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