Equivalence between the Osserman condition and the Rakić duality principle in dimension 4

Abstract

We show that four-dimensional Riemannian manifolds which satisfy the Rakić duality principle are Osserman (i.e. the eigenvalues of the Jacobi operator are constant). Thus, since it was proved in Rakić (1999) [9] that Osserman manifolds satisfy the Rakić duality principle, both conditions are equivalent.