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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.1068~1076


Projectively flat exponential Finsler metric

Author(s):  YU Yao-yong, YOU Ying

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   yuyaoyong@126.com

Key Words:  Exponential Finsler metric, Projectively flat, (&alpha, , &beta, )-metric, Douglas tensor

YU Yao-yong, YOU Ying. Projectively flat exponential Finsler metric[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1068~1076.

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publisher="Zhejiang University Press & Springer",

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T1 - Projectively flat exponential Finsler metric
A1 - YU Yao-yong
A1 - YOU Ying
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A1068

In this paper, we study a class of Finsler metric in the form F=αexp(&beta;/α)+εβ, where α is a Riemannian metric and &beta; is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and &beta; is parallel with respect to α. Moreover, we proved that the douglas tensor of exponential Finsler metric F vanishes if and only if &beta; is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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