Some results on strong Randers metrics

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• 作者：Xiaohuan Mo ; Hongmei Zhu
• 关键词：Complex Finsler manifold ; K?hler Randers metric ; Holomorphic sectional curvature ; 53C60 ; 53B40
• 刊名：Periodica Mathematica Hungarica
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：71
• 期：1
• 页码：24-34
• 全文大小：437 KB
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• 作者单位：Xiaohuan Mo (1)
  Hongmei Zhu (2)
  
  1. Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, China
  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2829

文摘

Let \(F:=\alpha +|\beta |\) be a strong Randers metric on a complex manifold. We show that \(F\) is K?hler if and only if \(\beta \) is parallel with respect to \(\alpha \). Furthermore if \(\alpha \) has constant holomorphic sectional curvature, we show that the following assertions are equivalent: (i) \(F\) is K?hler; (ii) \(F=|v|^{2}+\langle c,\bar{v}\rangle \) is a Minkowskian metric unless \(F\) is usually K?hlerian.