Holomorphic submersions of locally conformally K?hler manifolds

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• 作者：Liviu Ornea ; Maurizio Parton…
• 关键词：Locally conformally K?hler manifold ; Holomorphic submersion ; Vaisman manifold ; 53C55
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：193
• 期：5
• 页码：1345-1351
• 全文大小：129 KB
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• 作者单位：Liviu Ornea (1) (2)
  Maurizio Parton (3)
  Victor Vuletescu (1)
  
  1. Faculty of Mathematics, University of Bucharest, 14 Academiei str., 010014, Bucharest, Romania
  2. Institute of Mathematics “Simion Stoilow-of the Romanian Academy, 21, Calea Grivitei Street, 010702, Bucharest, Romania
  3. Dipartimento di Scienze, Universita di Chieti—Pescara, Pescara, Italy
  
• ISSN：1618-1891

文摘

A locally conformally K?hler (LCK) manifold is a complex manifold covered by a K?hler manifold, with the covering group acting by homotheties. We show that if such a compact manifold \(X\) admits a holomorphic submersion with positive-dimensional fibers at least one of which is of K?hler type, then \(X\) is globally conformally K?hler or biholomorphic, up to finite covers, to a small deformation of a Vaisman manifold (i.e., a mapping torus over a circle, with Sasakian fiber). As a consequence, we show that the product of a compact non-K?hler LCK and a compact K?hler manifold cannot carry a LCK metric.