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

http://doi.org/10.1631/jzus.2006.A2097


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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author="YU Yao-yong",
journal="Journal of Zhejiang University Science A",
volume="7",
number="12",
pages="2097-2103",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2097"
}

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%DOI 10.1631/jzus.2006.A2097

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T1 - Projectively flat arctangent Finsler metric
A1 - YU Yao-yong
J0 - Journal of Zhejiang University Science A
VL - 7
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SP - 2097
EP - 2103
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A2097


Abstract: 
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

Reference

[1] Bao, D., Robles, C., 2003. On Randers metrics of constant flag curvature. Reports on Mathematical Physics, 51(1):9-42.

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

[3] Chern, S.S., Shen, Z., 2005. Riemann-Finsler Geometry. World Scientific, p.53.

[4] Hamel, G., 1903. Über die Geometrieen in denen die Geraden die kürzestensind. Math. Ann., 57(2):231-264.

[5] Mo, X., Shen, Z., Yang, C., 2006. Some constructions of projectively flat Finsler metric. Science in China-Series A: Mathematics, 49(5):703-714.

[6] Shen, Y.B., Zhao, L.L., 2006. Some projectively flat (α,β)-metrics. Science in China-Series A: Mathematics, 49(6):838-851.

[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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