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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.6 P.963-968


Projectively flat Asanov Finsler metric

Author(s):  HAN Jing-wei, YU Yao-yong

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jingweih@126.com

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

HAN Jing-wei, YU Yao-yong. Projectively flat Asanov Finsler metric[J]. Journal of Zhejiang University Science A, 2007, 8(6): 963-968.

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author="HAN Jing-wei, YU Yao-yong",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

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%DOI 10.1631/jzus.2007.A0963

T1 - Projectively flat Asanov Finsler metric
A1 - HAN Jing-wei
A1 - YU Yao-yong
J0 - Journal of Zhejiang University Science A
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SP - 963
EP - 968
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0963

In this work, we study the Asanov Finsler metric F=α(&beta;2/α2+/α+1)1/2exp{(G/2)arctan[&beta;/()+G/2]}, where α=(&alpha;ijyiyj)1/2 is a Riemannian metric and &beta;=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 &beta; is parallel with respect to α. Moreover, we proved that the douglas tensor of Asanov Finsler metric vanishes if and only if &beta; is parallel with respect to α.

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


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