Osserman pseudo-Riemannian manifolds with diagonalizable Jacobi operators are studied. A classification of such manifolds is achieved under two conditions on the number of different eigenvalues of the Jacobi operators and their associated elgenspaces.
Agustin BONOME. Regina CASTRO. Eduardo GARCÍA-RÍO. Luis HERVELLA. Ramón VÁZQUEZ-LORENZO. "Pseudo-Riemannian manifolds with simple Jacobi operators." J. Math. Soc. Japan 54 (4) 847 - 875, October, 2002. https://doi.org/10.2969/jmsj/1191591994