Kragujevac J. Math. 28

Kragujevac J. Math. 28 - 6 Kragujevac J. Math. 28 (2005) 87-96.

CONFORMALLY OSSERMAN LORENTZIAN MANIFOLDS

Novica Blazic

Faculty of Mathematics, University of Belgrade,
P. O. Box 550, 11001 Belgrade, Serbia and Montenegro

Abstract. Let (Mⁿ,g) be a pseudo-Riemannian manifold of which the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit timelike (spacelike) tangent vectors (known as conformally Osserman manifolds). In this work we study the conformally Osserman Lorentzian manifolds. The established characterizations indicate the rigidity of conformally Osserman Lorentzian manifolds. We additionally illustrate that rigidity by reviewing analog recent characterizations in the case of metrics of other signatures.