N. Bla\v zi\'c, N. Bokan and Z. Raki\'c, University of Belgrade, Faculty of Mathematics, Studentski trg 16, p.p. 550, 11000 Belgrade, YUGOSLAVIA
E-mail: daleksee@esi.ac.at; fort@rsuh.ru
blazicn@matf.bg.ac.yu
neda@matf.bg.ac.yu
zrakic@matf.bg.ac.yu
Abstract. The main goal is to show that the pointwise Osserman four-dimensional pseudo-Riemannian manifolds (Lorentzian and manifolds of neutral signature $(--++)$) can be characterized as self dual (or anti-self dual) Einstein manifolds. Also, examples of pointwise Osserman manifolds which are not Osserman are discussed.
AMSclassification. 53B30, 53C50
Keywords. Self-dual manifolds, manifolds of neutral signature, Jacobi operator, Einstein manifolds