Complex Osserman Kähler manifolds in dimension four

Abstract

Let H be a 4-dimensional almost-Hermitian manifold which satisfies the Kähler identity. We show that H is complex Osserman if and only if H has constant holomorphic sectional curvature. We also classify in arbitrary dimensions all the complex Osserman Kähler models which do not have 3 eigenvalues. MSC 2000:53B35.