Four-dimensional Osserman symmetric spaces (Q5956150)

It is shown that locally symmetric four-dimensional Osserman spaces are flat, locally isometric to a rank-one symmetric space or locally isometric to certain rank-two symmetric spaces, the later corresponding to the situation when the Jacobi operator is not diagonalizable. The proof relies on a classification of locally symmetric neutral four-manifolds by \textit{A. Derdzinski} [Einstein metrics in dimension four, in: Handbook of Differential Geometry, Volume 1, Elsevier, Amsterdam, 419-707 (2000; Zbl 0991.53025)].