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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Zhao, Ll. On some projectively flat polynomial (α,β)-metrics. J. Zhejiang Univ. - Sci. A 8, 957–962 (2007). https://doi.org/10.1631/jzus.2007.A0957
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DOI: https://doi.org/10.1631/jzus.2007.A0957