The symmetry and the homogeneity in pseudo-Riemannian geometry

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We studied the following subjects on the symmetry and the homogeneity in pseudo-Riemannian geometry .We developed the classification problem of conformally flat homogeneous Lorentzian manifolds. For almost all types of the Ricci operators, we have solved the construction and the classification problem. We construct horocyclic surfaces in hyperbolic3-space associated with spacelike curves in the lightcone and classify their singularities using invariants of corresponding spacelike curves.