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数学进展 - 2020, Vol. 49(6): 723-736
研究论文
一类局部射影平坦的芬斯勒度量
A Class of Locally Projectively Flat Finsler Metrics

耿杰1, 宋卫东1, 2
GENG Jie1, SONG Weidong1, 2

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
1. College of General Education and Foreign Languages, Anhui Institute of Information Technology, Wuhu, Anhui, 241000, P. R. China;
2. College of Tencent Cloud Big Data, Ma'anshan University, Ma'anshan, Anhui, 243000, P. R.China

收稿日期: 2019-08-27
出版日期: 2020-11-17
2020, Vol. 49(6): 723-736
DOI: 10.11845/sxjz.2019092b


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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.
关键词 芬斯勒度量局部射影平坦球对称旗曲率    
Abstract: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.
Key wordsFinsler metric    locally projectively flat    spherically symmetric    flag curvature
PACS:  O186.14  
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