Equivariant embeddings of strongly pseudoconvex Cauchy–Riemann manifolds
- Let \(\it X\) be a CR manifold with transversal, proper CR action of a Lie group \(\it G\). We show that the quotient \(\it X/G\) 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 \(\it X/G\). We then use this result and complex geometry to prove an embedding theorem for (non-compact) strongly pseudoconvex CR manifolds with transversal \(\textit {G ⋊}\) \(S^1\)-action. The methods of the proof are applied to obtain a projective embedding theorem for compact CR manifolds.
| Author: | Kevin FritschORCiDGND, Peter HeinznerORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-97599 |
| DOI: | https://doi.org/10.1007/s00229-021-01291-w |
| Parent Title (English): | Manuscripta mathematica |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/03/20 |
| Date of first Publication: | 2021/03/28 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Volume: | 168 |
| First Page: | 137 |
| Last Page: | 163 |
| Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Mathematik |
| open_access (DINI-Set): | open_access |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
