Let , , be an n-dimensional homogeneous Lorentzian 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 Lorentzian manifolds). Then is a conformally Osserman Lorentzian manifold if and only if is a conformally flat manifold, (Blazic, 2005). In this paper, by utilizing this equivalence and the similar arguments in Erdogan and Ikawa (1995) and Sekigawa and Takagi (1971), we classify locally conformally flat homogeneous Lorentzian manifolds and, equivalently, as well as conformally Osserman Lorentzian manifolds which satisfy a condition on the Ricci tensor.
Key words: Conformally manifold, Weyl conformal tensor, conformally Osserman manifold, conformal Jacobi operator.
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