表題番号：2021C-525
日付：2022/03/27
研究課題多様体上のJacobi構造と整合する計量の構成
| 研究者所属（当時） | 資格 | 氏名 | |
|---|---|---|---|
| （代表者） | 理工学術院 基幹理工学部 | 助手 | 木村 直記 |
| （連携研究者） | 工学院大学 | 講師 | 中村 友哉 |
- 研究成果概要
- A Jacobi structure on a manifold is a generalization of both of a contact structure and a Poisson structure. Geometric properties of contact manifolds and Poisson manifolds are understood to some extent. Meanwhile, geometric properties of Jacobi manifolds are hardly understood. In studying geometric properties of manifolds with some geometric structures, it is often useful to introduce metrics which are compatible in some sense with those structures.
Tomoya Nakamura and I defined the compatibility between Jacobi structures and pseudo-Riemannian metrics by using the Levi-Civita connection of the metric. This compatibility is considered as a generalization of the compatibility between Poisson structures and pseudo-Riemannian metrics defined by Boucetta. We showed that this compatibility behaves well to the Poissonization of a Jacobi structure. In addition, we proved that if a contact metric structure is compatible, then it becomes a Sasaki structure. Hence our definition of the compatibility between Jacobi structures and metrics is regarded as a generalization of Sasaki structures.
We are writing a paper on these results and will submit it to an international academic journal.