A Note on Osserman Lorentzian Manifolds

Let p be a point of a Lorentzian manifold M. We show that ifM is spacelike Osserman at p, then M has constant sectionalcurvature at p; similarly, if M is timelike Osserman at p, thenM has constant sectional curvature at p. The reverse implicationsare immediate. The timelike case and 4-dimensional spacelikecase were first studied in 3]; we use a different approachto this case. 1991 Mathematics Subject Classification 53B30,53C50.