Four-dimensional Osserman metrics of neutral signature

Garcia-Rio, E.; Gilkey, P.; Vazquez-Abal, M. E.; Vazquez-Lorenzo, R.

Four-dimensional Osserman metrics of neutral signature

Authors

Description

In the algebraic context, we show that 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 of 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.