A study of the relation between Einstein-Weyl structures and almost contact metric structures

爱因斯坦-外尔结构与近接触度量结构关系的研究

• 批准号: 15540101
• 负责人: NARITA Fumio
• 金额: $ 0.64万
• 依托单位: Akita National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540101/
• 关键词: Weyl manifold; Weyl submersion; Einstein-Weyl manifold; Canonical variation; Pseudo-Schwarzian; Conformal transformation; ワイル多様体; ワイルしずめ込み; アインシュタイン・ワイル多様体; 擬シュバルツテンソル

I used an idea of the Weyl submersion for a research of the Einstein-Weyl structure of a Weyl manifold. For a Weyl submersion with Weyl totally geodesic fibers, I obtained a necessary and sufficient condition for a Weyl structure of the total space to admits an Einstein-Weyl structure. By using its result, I investigated the Einstein-Weyl structure of an η-Einstein contact metric manifold. Moreover, I studied Einstein-Weyl structures of a canonical variation of the total space of a Weyl submersion with Weyl totally geodesic fibers.Next, for a Weyl manifold with a torsion-free affine connection, using the pseudo-Schwarzian tensor I investigated some invariants which do not vary under conformal transformations or Mobius transformations.

我用外尔浸没的概念来研究外尔流形的Einstein-Weyl结构。对于具有Weyl全测地纤维的Weyl浸没，得到了全空间的Weyl结构存在Einstein-Weyl结构的一个充要条件.利用它的结果，研究了η-Einstein接触度规流形的Einstein-Weyl结构.其次，对于具有挠率自由仿射联络的Weyl流形，利用伪Schwarzian张量，研究了在保角变换或Mobius变换下不变的一些不变量。