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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2097-2103


Projectively flat arctangent Finsler metric

Author(s):  YU Yao-yong

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   yuyaoyong@126.com

Key Words:  Arctangent Finsler metric, Projectively flat, (&alpha, , &beta, )-metric, Flag curvature

YU Yao-yong. Projectively flat arctangent Finsler metric[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2097-2103.

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publisher="Zhejiang University Press & Springer",

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T1 - Projectively flat arctangent Finsler metric
A1 - YU Yao-yong
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A2097

In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (&alpha;,&beta;)-metric, where α is a Riemannian metric and &beta; is a 1-form. We obtain a sufficient and necessary condition that F is locally projectively flat if and only if α and &beta; satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively flat. Moreover, we prove that such projectively flat Finsler metrics with constant flag curvature must be locally Minkowskian.

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


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[2] Bryant, R., 2002. Some remarks on Finsler manifolds with constant flag curvature. Houston J. Math., 28(2):221-262.

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[7] Shen, Z., 2003. Projectively flat Randers metrics of constant curvature. Math. Ann., 325(1):19-30.

[8] Shen, Z., 2004. Landsberg Curvature, S-Curvature and Riemann Curvature, in a Sampler of Riemann-Finsler Geometry. MSRI Series Vol. 50, Cambridge University Press, p.303-355.

[9] Shen, Z., 2006. On Some Projectively Flat Finsler Metrics. Http://www.math.iupui.edu/~zshen/Research/papers/ConstructionsOfProjectivelyFlatMetrics.pdf.

[10] Shen, Z., Civi Yildirim, G., 2005. On a class of projectively flat metrics of constant flag curvature. Canadian Journal of Math. (in Press). Http://www.math.iupui.edu/~zshen/Research/papers/ProjectivelyFlatMetricsShenYildirim.pdf.

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