Four Dimensional Osserman Lorentzian Manifolds
A problem of Osserman related to the constancy of the eigenvalues of the Jacobi operator is studied in Lorentzian Geometry. It is proven that pointwise timelike Osserman Lorentzian manifolds are of constant curvature as well as those of pointwise spacelike Osserman Lorentzian spaces of dimension 3 and 4. It is shown that a 4-dimensional globally null Osserman Lorentzian manifold is either of constant curvature or is locally a Robertson-Walker spacetime.
Mathematics Subject Classification53B30 53C50
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