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. Projectively flat arctangent Finsler metric[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2097-2103.
@article{title="Projectively flat arctangent Finsler metric",
author="YU Yao-yong",
journal="Journal of Zhejiang University Science A",
volume="7",
number="12",
pages="2097-2103",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2097"
}
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%T Projectively flat arctangent Finsler metric
%A YU Yao-yong
%J Journal of Zhejiang University SCIENCE A
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%P 2097-2103
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%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A2097
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T1 - Projectively flat arctangent Finsler metric
A1 - YU Yao-yong
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 12
SP - 2097
EP - 2103
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A2097
Abstract: In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α,β)-metric, where α is a Riemannian metric and β is a 1-form. We obtain a sufficient and necessary condition that F is locally projectively flat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively flat. Moreover, we prove that such projectively flat Finsler metrics with constant flag curvature must be locally Minkowskian.
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