论文标题
减少适当行动的原则
Reduction principles for proper actions
论文作者
论文摘要
让$ g $成为一个谎言组，在平滑的歧管$ m $上正确起作用。如果连接了$ m/g $，那么我们将展示一些简单而基本的结构，以进行适当的操作。特别是，我们证明，紧凑型转换组中的还原原理具有适当的行动。作为一种应用，我们证明，还原原理适用于极地作用和对谎言组的等轴测动作的整体不变，这称为共光，这衡量了动作的极地。我们还研究了符号动作。因此，我们假设$（m，ω）$是符号歧管，而$ m $ $ $ $ $ $ g $ castion $ $ preserves $ω$。 ％如果$ g $是Abelian，我们将结果概括为\ cite {ben，dp1，dp2}}的主要结果是共智动作的等效定理，概括\ cite \ cite [theorem 3 p.267] {hw}。最后，我们完全表征了在\ cite {pg}中证明结果的Asystatic动作。
Let $G$ be a Lie group acting properly on a smooth manifold $M$. If $M/G$ is connected, then we exhibit some simple and basic constructions for proper actions. In particular, we prove that the reduction principle in compact transformation groups holds for proper actions. As an application, we prove that a reduction principle holds for polar actions and for the integral invariant for isometric actions of Lie groups, called copolarity, which measures how far from being polar the action is. We also investigate symplectic actions. Hence we assume that $(M,ω)$ is a symplectic manifold and the $G$ action on $M$ preserves $ω$. %If $G$ is Abelian, we generalize results proved in \cite{Ben,DP1,DP2} The main result is the Equivalence Theorem for coisotropic actions, generalizing \cite[Theorem 3 p.267]{HW}. Finally, we completely characterize asystatic actions generalizing results proved in \cite{pg}.
