CLC number: O186.1
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Received: 2006-07-17
Revision Accepted: 2007-01-31
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HAN Jing-wei, YU Yao-yong. Projectively flat Asanov Finsler metric[J]. Journal of Zhejiang University Science A, 2007, 8(6): 963-968.
@article{title="Projectively flat Asanov Finsler metric",
author="HAN Jing-wei, YU Yao-yong",
journal="Journal of Zhejiang University Science A",
volume="8",
number="6",
pages="963-968",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0963"
}
%0 Journal Article
%T Projectively flat Asanov Finsler metric
%A HAN Jing-wei
%A YU Yao-yong
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 6
%P 963-968
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0963
TY - JOUR
T1 - Projectively flat Asanov Finsler metric
A1 - HAN Jing-wei
A1 - YU Yao-yong
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 6
SP - 963
EP - 968
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A0963
Abstract: In this work, we study the Asanov Finsler metric F=α(β2/α2+gβ/α+1)1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(−2,2), h=(1−g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.
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