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Received: 2006-10-13

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.6 P.957-962

http://doi.org/10.1631/jzus.2007.A0957


On some projectively flat polynomial (α,β)-metrics


Author(s):  ZHAO Li-li

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

Corresponding email(s):   shally523@163.com

Key Words:  Finsler metric, Polynomial, Projectively flat


ZHAO Li-li. On some projectively flat polynomial (α,β)-metrics[J]. Journal of Zhejiang University Science A, 2007, 8(6): 957-962.

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author="ZHAO Li-li",
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volume="8",
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year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0957"
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T1 - On some projectively flat polynomial (α,β)-metrics
A1 - ZHAO Li-li
J0 - Journal of Zhejiang University Science A
VL - 8
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SP - 957
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%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0957


Abstract: 
In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a finsler metric in the form F=α+a1β+a2β2/α+a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of finsler metrics.

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Reference

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[7] Mo, X., Shen, Z., Yang, C., 2006. Some constructions of projectively flat Finsler metrics. Sci. in China (Ser. A), 49(5):703-714.

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[11] Shen, Z., Civi Yildirim, G., 2005. On a class of projectively flat metrics of constant flag curvature. Can. J. Math., in press.

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