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arXiv · 2002.00219

Equivariant embeddings of strongly pseudoconvex Cauchy-Riemann manifolds

Kevin Fritsch·Peter Heinzner
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Abstract

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.

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Kevin Fritsch, Peter Heinzner. 2020-02-01. Equivariant embeddings of strongly pseudoconvex Cauchy-Riemann manifolds. https://arxiv.org/abs/2002.00219

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