Abstract
AbstractLet X be a CR manifold with transversal, proper CR action of a Lie group G. We show that the quotient 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 factorizes uniquely over a holomorphic map on X/G. We then use this result and complex geometry to prove an embedding theorem for (non-compact) strongly pseudoconvex CR manifolds with transversal $$G \rtimes S^1$$
G
⋊
S
1
-action. The methods of the proof are applied to obtain a projective embedding theorem for compact CR manifolds.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Andreotti, A., Fredricks, G.A.: Embeddability of real analytic Cauchy–Riemann manifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. 6(2), 285–304 (1979)
2. Baouendi, M.S., Rothschild, L.P., Treves, F.: CR structures with group action and extendability of CR functions. Invent. Math. 82, 359–396 (1985)
3. Borel, A.: Représentations de groupes localement compacts. Springer, Berlin (1972)
4. Boutet de Monvel, L.: Intégration des équations de Cauchy–Riemann induites formelles, Sémin. Équ. Dériv. Partielles (9), 1–13 (1974–1975)
5. Fornaess, J., Narasimhan, R.: The Levi problem on complex spaces with singularities. Math. Ann. 248, 47–72 (1980)