CLC number: O186
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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YU Yao-yong, YOU Ying. Projectively flat exponential Finsler metric[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1068-1076.
@article{title="Projectively flat exponential Finsler metric",
author="YU Yao-yong, YOU Ying",
journal="Journal of Zhejiang University Science A",
volume="7",
number="6",
pages="1068-1076",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1068"
}
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%T Projectively flat exponential Finsler metric
%A YU Yao-yong
%A YOU Ying
%J Journal of Zhejiang University SCIENCE A
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%N 6
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%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1068
TY - JOUR
T1 - Projectively flat exponential Finsler metric
A1 - YU Yao-yong
A1 - YOU Ying
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 6
SP - 1068
EP - 1076
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1068
Abstract: In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β 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 β is parallel with respect to α. Moreover, we proved that the douglas tensor of exponential Finsler metric F vanishes if and only if β 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.
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