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CLC number: O186.1

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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


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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A1 - ZHAO Li-li
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0957

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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