| On some projectively flat polynomial （α,β）-metrics |
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| 作者姓名： | ZHAO Li-li |
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| 作者单位： | ZHAO Li-li1，2 (1Department of Mathematics，Zhejiang University，Hangzhou 310027，China) (2Department of Mathematics，Shanghai Jiao Tong University，Shanghai 200240，China) |
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| 基金项目： | ACKN0WLEDGEMENTS The author is grateful to Professor Yibing Shen and Professor Zhongmin Shen for providing helpful comments which led to a significant improvement of this article. |
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| 摘 要： | 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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| 关 键 词： | 射影平坦 多项式 Finsler度量 充要条件 |
| 收稿时间： | 2006-10-13 |
| 修稿时间： | 2007-01-16 |
On some projectively flat polynomial (<Emphasis Type="Italic">α</Emphasis>,<Emphasis Type="Italic">β</Emphasis>)-metrics |
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| ZHAO Li-li.On some projectively flat polynomial (α,β)-metrics[J].Journal of Zhejiang University Science,2007,8(6):957-962. |
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| Authors: | Zhao Li-li |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China;(2) Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China |
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| 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+α
1
β+α
2
β
2/α+α
4
β
4/α
3 to be projectively flat, where α
i (i=1,2,4) are constants with α
1≠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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| Keywords: | Finsler metric Polynomial Projectively flat |
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