Conformally Osserman manifolds

Abstract

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension $n\ne 3,4,16$ is locally conformally equivalent either to a Euclidean space or to a rank-one symmetric space.

23 pages