Four-dimensional Osserman-Ivanov-Petrova metrics of neutral signature

摘要

Algebraic curvature tensors which are Osserman-IP in the (--++)-signature setting are completely determined. As a consequence, it is shown that a four-dimensional pointwise Osserman-IP manifold is a space of constant sectional curvature or, otherwise, at each point the Jacobi operators either vanish or they are two-step nilpotent.