| Title: | Complete nonsingular holomorphic foliations on Stein manifolds |
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| Authors: | ID Alarcón, Antonio (Author)
ID Forstnerič, Franc (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s00009-023-02566-0
 PDF - Presentation file, download (433,06 KB)
MD5: B229C13B5436695289C88D0816A94778
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Let $X$ be a Stein manifold of complex dimension $n \ge 1$ endowed with a Riemannian metric ${\mathfrak g}$. We show that for every integer $k$ with $\left[\frac{n}{2}\right] \le k \le n-1$ there is a nonsingular holomorphic foliation of dimension $k$ on $X$ all of whose leaves are topologically closed and ${\mathfrak g}$-complete. The same is true if $1\le k \left[\frac{n}{2}\right]$ provided that there is a complex vector bundle epimorphism $TX\to X \times \mathbb{C}^{n-k}$. We also show that if $\mathcal{F}$ is a proper holomorphic foliation on $\mathbb{C}^n$ $(n > 1)$ then for any Riemannian metric ${\mathfrak g}$ on $\mathbb{C}^n$ there is a holomorphic automorphism $\Phi$ of $\mathbb{C}^n$ such that the image foliation $\Phi_*\mathcal{F}$ is ${\mathfrak g}$-complete. The analogous result is obtained on every Stein manifold with Varolin's density property. |
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| Keywords: | Stein manifolds, complete holomorphic foliations, density property |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 21, iss. 1, article no. 25 |
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| PID: | 20.500.12556/DiRROS-18206  |
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| UDC: | 517.5 |
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| ISSN on article: | 1660-5446 |
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| DOI: | 10.1007/s00009-023-02566-0 |
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| COBISS.SI-ID: | 183749123 |
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| Note: |
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| Publication date in DiRROS: | 19.02.2024 |
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| Views: | 568 |
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| Downloads: | 239 |
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