2022/10/01 更新

写真a

キムラ ナオキ
木村 直記
所属
理工学術院 基幹理工学部
職名
助手
 

特定課題研究

  • 多様体上のJacobi構造と整合する計量の構成

    2021年   中村 友哉

     概要を見る

    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.