一类射影平坦和对偶平坦的Finsler度量

doi:10.3969/j.issn.0253-2778.2017.06.002

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (6): 459-464.DOI: 10.3969/j.issn.0253-2778.2017.06.002

一类射影平坦和对偶平坦的Finsler度量

何超，李影，宋卫东

安徽师范大学数学计算机科学学院，安徽芜湖 241000)

收稿日期:2016-03-10 修回日期:2016-12-04 出版日期:2017-06-30 发布日期:2017-06-30

A class of projectively flat and dually flat Finsler metrics

HE Chao, LI Ying, SONG Weidong

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

Received:2016-03-10 Revised:2016-12-04 Online:2017-06-30 Published:2017-06-30
Contact: SONG Weidong
About author:HE Chao, male, born in 1992, master. Research field: Differential geometry. E-mail: begondjames@163.com
Supported by:
Supported by the National Natural Science Foundation of China (11371032).

摘要/Abstract

摘要： Finsler几何是没有二次型限制的黎曼几何，Finsler几何中两个非常重要的问题是射影平坦和对偶平坦的Finsler度量.主要研究了一类含有3个参数的Finsler度量，得到了其为射影平坦和对偶平坦的充要条件.

关键词: Finsler度量, 球对称, 射影平坦, 对偶平坦

Abstract: Finsler geometry is just Riemannian geometry without quadratic restriction, and the projectively flat and dually flat Finsler metrics are very important in Finsler geometry. Here a class of 3-parameter of Finsler metrics were studied, and the necessary and sufficient conditions for the Finsler metrics to be projectively flat and dually flat were obtained.

Key words: Finsler metrics, spherically symmetric, projectively flat, dually flat

中图分类号:

O186.12

何超，李影，宋卫东. 一类射影平坦和对偶平坦的Finsler度量[J]. 中国科学技术大学学报, 2017, 47(6): 459-464.

HE Chao, LI Ying, SONG Weidong. A class of projectively flat and dually flat Finsler metrics[J]. Journal of University of Science and Technology of China, 2017, 47(6): 459-464.

[1]	刘敏，宋卫东. 具有标量旗曲率的球对称Finsler度量[J]. 中国科学技术大学学报, 2019, 49(3): 199-202.
[2]	华义平，宋卫东. 一类局部对偶平坦的(α,β)度量[J]. 中国科学技术大学学报, 2018, 48(11): 885-889.

一类射影平坦和对偶平坦的Finsler度量

A class of projectively flat and dually flat Finsler metrics

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