论文标题
强烈的伪有源cauchy-riemann歧管的嵌入
Equivariant embeddings of strongly pseudoconvex Cauchy-Riemann manifolds
论文作者
论文摘要
令$ x $为具有横向，适当的Cr $ g $ Action的CR歧管。我们表明$ x/g $是一个复杂的空间，因此商映射是CR地图。此外，商是通用的，即，每个不变的cr映射成复杂的流形因子，都可以在$ x/g $上的全态映射上唯一地唯一。然后，我们使用此结果和复杂的几何形状来证明（非压缩）具有横向$ g \ rtimes s^1 $ Action的嵌入定理。使用证明的方法用于获取用于紧凑型CR歧管定理的投射嵌入。
Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold factorises uniquely over a holomorphic map on $X/G$. We then use this result and complex geometry to proof an embedding theorem for (non-compact) strongly pseudoconvex CR manifolds with transversal $G \rtimes S^1$-action. The methods of the proof are applied to obtain a projective embedding theorem for compact CR manifolds.
