Finsler流形的Reeb向量场的一些注记  

A Note on the Reeb Vector Field of a Finsler Manifold

作　　者：李娜[1] 李明[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《西南大学学报（自然科学版）》2014年第8期97-100,共4页Journal of Southwest University(Natural Science Edition)

基　　金：重庆市科委自然科学基金项目(cstc2011jjA00026);重庆市教委自然科学基金项目(Kj130824)

摘　　要：首先研究了Finsler流形的射影球丛上的Reeb向量场的若干基本几何性质.应用Reeb向量场的基本性质,得到Reeb向量场满足的两个几何不等式,其中等号成立的充要条件是Finsler流形具有常旗曲率1.In this paper, some geometric properties of the Reeb vector field of a Finsler manifold are proved. Based on the basic properties, two geometric inequalities related to the Reeb vector field are giv en, and the necessary and sufficient condition for the equalities of the two inequalities is established, i. e. their equalities hold if and only if the Finsler manifold is of constant flag curvature 1.

关 键 词：FINSLER流形 Reeb向量场 旗曲率 

分 类 号：O186.1[理学—数学]