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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2007, Vol. 8 Issue (6): 957-962    DOI: 10.1631/jzus.2007.A0957
Computational Mathematics     
On some projectively flat polynomial (α,β)-metrics
ZHAO Li-li
Department of Mathematics, Zhejiang University, Hangzhou 310027, China; 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+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.

Key words： Finsler metric      Polynomial      Projectively flat     
Received: 13 October 2006     
CLC:  O186.1  
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ZHAO Li-li
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ZHAO Li-li. On some projectively flat polynomial (α,β)-metrics. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(6): 957-962.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2007.A0957     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2007/V8/I6/957

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