Four-dimensional Osserman metrics of neutral signature (Q1047582)

The authors describe \(4\) dimensional Osserman metrics of neutral signature \((2,2)\). From an algebraic point of view, they obtain that null Osserman, space-like Osserman and time-like Osserman are equivalent conditions for a model of signature \((2,2)\). They completely classify the null Jordan Osserman models of neutral signature. In the geometric context, the authors show that a pseudo-Riemannian \(4\) dimensional manifold with signature \((2,2)\) is null Jordan Osserman if and only if either it has constant sectional curvature or it is locally a complex space form.