单群和横截结构的等距作用：可积正规情形
Isometric actions of simple groups and transverse structures: The integrable normal case
摘要：
对于连通非紧单李群$G$中具有稠密轨道的作用，当作用保持一定的几何结构时，我们得到了一些整体刚性的结果。特别地，我们证明了对于一个$G$ -作用与$(G\times K\backslash H)/Γ$形式的空间上的作用等价，$G$ -作用保持伪黎曼度量和横截黎曼度量到轨道是充分必要的.一个类似的结果证明了$(G\times H)/Γ$形式的空间上的$G$ -作用的特征在于保持横向平行性。通过将我们的技术与作用的代数壳的概念相联系，我们得到了$G$作用于某些几何流形上的无穷小李代数结构。
英文摘要：
For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to one on a space of the form $(G\times K\backslash H)/Γ$, it is necessary and sufficient for the $G$-action to preserve a pseudo-Riemannian metric and a transverse Riemannian metric to the orbits. A similar result proves that the $G$-actions on spaces of the form $(G\times H)/Γ$ are characterized by preserving transverse parallelisms. By relating our techniques to the notion of the algebraic hull of an action, we obtain infinitesimal Lie algebra structures on certain geometric manifolds acted upon by $G$.
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