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Conformally flat Lorentzian three-spaces with various properties of symmetry and homogeneity. (English) Zbl 1240.53116

The paper studies conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric and provides a complete classification of those which are locally homogeneous or curvature homogeneous. Some pseudo-symmetric Lorentzian three-manifolds which are not curvature homogeneous are also described. Finally, higher dimensional semi-symmetric examples are constructed as real cones over pseudo-Riemannian space forms of curvature different from \(-1\).

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C35 Differential geometry of symmetric spaces
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