Equivariant embeddings of strongly pseudoconvex Cauchy-Riemann manifolds

2020/02/01 by Fritsch, Kevin, Heinzner, Peter
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.00219

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 S¹-action. The methods of the proof are applied to obtain a projective embedding theorem for compact CR manifolds.

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