Geometric structure on geometric manifolds which admit Lie group transformations and various Rigidity

我们审查了以下项目。(1)共形Fefferman-Lorentz流形的几何和拓扑方法。(1)证明了Obata-Ferrand定理对Lorentz流形的类似。(2)证明了Kuiper问题，即如果展开映射在S^<n-1,1>的泛覆盖上不是满射，那么在因果向量场存在的条件下，它是其像上的覆盖映射。(2)研究了混合型封闭非球面流形的下纤空间结构和光滑刚度。作为应用，证明了紧致非球面齐次流形的光滑刚性。

We have examined the following projects.(1) Approach from geometry and topology concerning conformally Fefferman-Lorentz manifolds.(1) We proved the analogue of the Obata-Ferrand theorem to Lorentz manifolds.(2) We proved the Kuiper's problem that if the developing map is not surjective on the universal cover of S^<n-1,1>, then it is a covering map onto its image under the existence of causal vector fields.(2) We studied the infrasolv-fiber space structure and the smooth rigidity on the closed aspherical manifolds of the mixed type. As an application, we proved the smooth rigidity of compact aspherical homogeneous manifolds.