The symmetry and the homogeneity in pseudo-Riemannian geometry

我们研究了伪黎曼几何中的对称性和齐次性。研究了共形平坦齐次洛伦兹流形的分类问题。对于几乎所有类型的Ricci算子，我们都解决了构造和分类问题。我们在双曲空间中构造了与光锥上的类空间曲线相关的环曲面，并利用相应的类空间曲线的不变量对其奇异性进行了分类。

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.