Quaternionic Kaehler manifolds and a curvature characterization of two- point homogeneous spaces (Q757863)

The Osserman conjecture says that a nonflat Riemannian manifold is locally symmetric of rank one if the curvature operator \(K_ v=R(\cdot,v)v\) for any unit vector \(v\in TM\) has constant eigenvalues, counting multiplicities. The author has shown in his previous paper that the Osserman conjecture is true if the dimension of the manifold (M,g) is 4, or \(2n+1\), or \(4n+2\), or if (M,g) is a Kaehler manifold of nonnegative (or non-positive) curvature. In the present paper the case of quaternionic Kaehler manifolds is studied and the Osserman conjecture is verified under some additional assumption, e.g., if the maximal (or minimal, respectively) eigenvalue of \(K_ v\) has multiplicity 3.