{"title":"满足 Stein Manifold 上奥卡-格劳尔特原理的非ramified 黎曼域","authors":"Makoto Abe, Shun Sugiyama","doi":"10.1007/s12220-024-01756-w","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\((D, \\pi )\\)</span> be an unramified Riemann domain over a Stein manifold of dimension <i>n</i>. Assume that <span>\\(H^k(D,\\mathscr {O}) = 0\\)</span> for <span>\\(2 \\le k \\le n - 1\\)</span> and there exists a complex Lie group <i>G</i> of positive dimension such that all differentiably trivial holomorphic principal <i>G</i>-bundles on <i>D</i> are holomorphically trivial. Then, we prove that <i>D</i> is Stein.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"2011 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unramified Riemann Domains Satisfying the Oka–Grauert Principle over a Stein Manifold\",\"authors\":\"Makoto Abe, Shun Sugiyama\",\"doi\":\"10.1007/s12220-024-01756-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\((D, \\\\pi )\\\\)</span> be an unramified Riemann domain over a Stein manifold of dimension <i>n</i>. Assume that <span>\\\\(H^k(D,\\\\mathscr {O}) = 0\\\\)</span> for <span>\\\\(2 \\\\le k \\\\le n - 1\\\\)</span> and there exists a complex Lie group <i>G</i> of positive dimension such that all differentiably trivial holomorphic principal <i>G</i>-bundles on <i>D</i> are holomorphically trivial. Then, we prove that <i>D</i> is Stein.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"2011 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Geometric Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12220-024-01756-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01756-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
假设 \(H^k(D,\mathscr {O}) = 0\) for\(2 \le k \le n - 1\) 并且存在一个正维度的复数李群 G，使得 D 上所有微分琐碎的全形主 G 束都是全形琐碎的。那么，我们证明 D 是 Stein。
Unramified Riemann Domains Satisfying the Oka–Grauert Principle over a Stein Manifold
Let \((D, \pi )\) be an unramified Riemann domain over a Stein manifold of dimension n. Assume that \(H^k(D,\mathscr {O}) = 0\) for \(2 \le k \le n - 1\) and there exists a complex Lie group G of positive dimension such that all differentiably trivial holomorphic principal G-bundles on D are holomorphically trivial. Then, we prove that D is Stein.
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