发表机构
Masaryk University; University of New England; Institute for Basic Science, Center for Complex Geometry（马萨里克大学; 新英格兰大学; 基础科学研究院，复几何中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究基于CR几何正规形技术，利用Bochner-Kähler流形与刚性球面Sasakian流形的对应关系，导出Bochner-Kähler势的典范公式并简化相关结果证明，还给出大量实例。
AI 中文摘要
我们引入了一种基于CR几何中正规形技术研究Bochner-Kähler流形的新方法。正如Webstone所观察到的，Bochner-Kähler流形与球面Sasakian流形密切相关。我们的方法利用了这种关系以及球面Sasakian流形（称为刚性球面）的正规形。在此设定下，Bochner-Kähler流形的势就是刚性正规形下刚性球面的定义方程。这为Bochner-Kähler势导出了一个典范公式，同时也为Bochner-Kähler流形的结构与对称性的已知结果提供了简化证明。我们的方法还通过相应Kähler势的隐式公式给出了大量实例。
英文摘要
We introduce a new approach to the study of Bochner-Kähler manifolds, based on normal form techniques in CR geometry. As observed by Webster, Bochner-Kähler manifolds are intimately related to spherical Sasakian manifolds. Our approach utilises this relationship as well as normal forms for spherical Sasakian manifolds (known as rigid spheres). In this setting potentials of Bochner-Kähler manifolds are nothing but the defining equations of rigid spheres in rigid normal form. This leads to a canonical formula for Bochner-Kähler potentials, as well as streamlined proofs of known results on the structure and the symmetries of Bochner-Kähler manifolds. Our approach also provides a host of examples in terms of an implicit formula of the corresponding Kähler potentials.
Comments32 pages, ancillary files include 2 Jupyter notebooks supplementing section 6
