一类局部射影平坦的芬斯勒度量  

A Class of Locally Projectively Flat Finsler Metrics

作　　者：耿杰 宋卫东 GENG Jie;SONG Weidong(College of General Education and Foreign Languages,Anhui Institute of Information Technology,Wuhu,Anhui,241000,P.R.China;College of Tencent Cloud Big Data,Ma’anshan University,M a’anshan,Anhui,243000,P.R.China)

机构地区：[1]安徽信息工程学院通识教育与外国语学院,芜湖安徽241000 [2]马鞍山学院腾讯云大数据学院,马鞍山安徽243000

出　　处：《数学进展》2020年第6期723-736,共14页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11071005);Quality Engineering Project of Anhui Province(No.2018yljc146);Teaching Research Major Project of Anhui Province(No.2017jyxm0947);Teaching Research Major Project of Anhui Institute of Information Technology(No.2017xjcgpy02)。

摘　　要：局部射影平坦芬斯勒度量的构造是芬斯勒几何研究中的一个重要问题.本文通过对球对称芬斯勒度量成为射影平坦芬斯勒度量所满足的偏微分方程进行研究,得到了局部射影平坦芬斯勒度量的新例子.进一步,给出了局部射影平坦的球对称芬斯勒度量的旗曲率.The construction of locally projectively flat Finsler metrics is an important problem in the study of Finsler geometry.In this paper,we study the partial differential equation equivalent to spherically symmetric Finsler metric being locally projectively flat,and obtain new examples of locally projectively flat Finsler metrics.Furthermore,we give the flag curvatures of spherically symmetric Finsler metrics which are locally projectively flat.

关 键 词：芬斯勒度量 局部射影平坦 球对称 旗曲率 

分 类 号：O186.14[理学—数学]