Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues

Abstract

Conformal Osserman four-dimensional manifolds are studied with special attention to the construction of new examples showing that the algebraic structure of any such curvature tensor can be realized at the differentiable level. As a consequence one gets examples of anti-self-dual manifolds whose anti-self-dual curvature operator has complex eigenvalues.