The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917527517396992 |
|---|---|
| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | Let \(\overline Ω\) be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let \(h:Z\to \overline Ω\) be a fibre bundle of Hölder-Zygmund class \(Λ^r\), \(r>0\), which is holomorphic over \(Ω\). Assuming that the fibre is an Oka manifold, we prove that every continuous section \(f_0:\overline Ω\to Z\) is homotopic to a section \(f_1:\overline Ω\to Z\) of class \(Λ^r(\overline Ω)\) which is holomorphic on \(Ω\). We also establish the parametric h-principle in this context. As an application, we obtain the Oka principle for the classification of vector bundles and principal bundles of Hölder-Zygmund classes on such domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains Forstneric, Franc Complex Variables Primary 32Q56, secondary 32L05, 32T15, 46J15 Let \(\overline Ω\) be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let \(h:Z\to \overline Ω\) be a fibre bundle of Hölder-Zygmund class \(Λ^r\), \(r>0\), which is holomorphic over \(Ω\). Assuming that the fibre is an Oka manifold, we prove that every continuous section \(f_0:\overline Ω\to Z\) is homotopic to a section \(f_1:\overline Ω\to Z\) of class \(Λ^r(\overline Ω)\) which is holomorphic on \(Ω\). We also establish the parametric h-principle in this context. As an application, we obtain the Oka principle for the classification of vector bundles and principal bundles of Hölder-Zygmund classes on such domains. |
| title | The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains |
| topic | Complex Variables Primary 32Q56, secondary 32L05, 32T15, 46J15 |
| url | https://arxiv.org/abs/2602.12598 |