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Received: 2006-10-13
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On some projectively flat polynomial (α,β)-metrics
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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",
journal="Journal of Zhejiang University Science A",
volume="8",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0957"
}
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T1 - On some projectively flat polynomial (α,β)-metrics
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J0 - Journal of Zhejiang University Science A
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EP - 962
%@ 1673-565X
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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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