FOUR-DIMENSIONAL OSSERMAN METRICS OF NEUTRAL SIGNATURE

摘要

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.