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Four Dimensional Osserman Lorentzian Manifolds

  • Eduardo García-Río
  • Demir N. Kupeli
Part of the Mathematics and Its Applications book series (MAIA, volume 350)

Abstract

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 Classification

53B30 53C50 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Eduardo García-Río
    • 1
  • Demir N. Kupeli
    • 2
  1. 1.Departamento de Análise Matemática, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiagoSpain
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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