论文标题
简单谎言组对伪河流流形的局部和全球刚度
Local and global rigidity for isometric actions of simple Lie groups on pseudo-Riemannian manifolds
论文作者
论文摘要
令$ m $成为有限的卷分析伪里曼尼亚人的歧管，该歧管承认具有密集轨道的等距$ g $ action，其中$ g $是一个连接的非紧凑型简单的谎言组。 For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the normal bundle to the $G$-orbits is non-integrable and for suitable conditions, we prove that $M$ has a $G$-invariant metric which is locally isometric to a Lie group with a bi-invariant metric (local rigidity theorem).后者不需要像以前的工作那样完成$ m $。我们还证明了一个总体结果表明，当我们假设$ m $完整（全球刚性定理）时，$ m $是$ h/γ$（$ h $中的$γ$ lattice）的形式的有限覆盖物。对于本地和全球刚度定理，我们提供的情况暗示了$ g $ actions $ g $ g $的刚度，由$ \ mathrm {so} _0（p，q）$，$ g_ {2（2）$或非compact $ f_4 $ for $ \ m mathbbbb {r} $。我们还调查了与这项工作有关的技术和结果。
Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the normal bundle to the $G$-orbits is non-integrable and for suitable conditions, we prove that $M$ has a $G$-invariant metric which is locally isometric to a Lie group with a bi-invariant metric (local rigidity theorem). The latter does not require $M$ to be complete as in previous works. We also prove a general result showing that $M$ is, up to a finite covering, of the form $H/Γ$ ($Γ$ a lattice in the group $H$) when we assume that $M$ is complete (global rigidity theorem). For both the local and the global rigidity theorems we provide cases that imply the rigidity of $G$-actions for $G$ given by $\mathrm{SO}_0(p,q)$, $G_{2(2)}$ or a non-compact simple Lie group of type $F_4$ over $\mathbb{R}$. We also survey the techniques and results related to this work.
