In the algebraic context, we show null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2, 2). We also classify the null Jordan Osserman models of signature (2, 2). In the geometric context, we show that a pseudo-Riemannian manifold with this signature is null Jordan Osserman if and only if either it has constant sectional curvature or it is locally a complex space form.
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