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A Class of Finsler Metrics with Bounded Cartan Torsion

Published online by Cambridge University Press:  20 November 2018

Xiaohuan Mo  and
Linfeng Zhou
Xiaohuan Mo
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China e-mail: [email protected]
Linfeng Zhou
Affiliation:
Department of Mathematics, East China Normal University, 200241 Shanghai, P.R. China e-mail: [email protected]
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Abstract

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In this paper, we find a class of $\left( \alpha ,\,\beta \right)$ metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.

Keywords

58E20Finsler manifold(α, β) metricCartan torsionR-quadraticflag curvature
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 1 , 01 March 2010 , pp. 122 - 132
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Bao, D. and Chern, S. S., A note on the Gauss-Bonnet theorem for Finsler spaces. Ann. Math. 143(1996), no. 2, 233–252. doi:10.2307/2118643Google Scholar
[2] Bao, D., Chern, S. S., and Shen, Z., An Introduction to Riemann-Finsler Geometry. Graduate Texts inh Mathematics 200, Springer-Verlag, New York, 2000.Google Scholar
[3] Bao, D., Robles, C., and Shen, Z., Zermelo navigation on Riemannian manifolds. J. Differential Geom. 66(2004), no. 3, 377–435.Google Scholar
[4] Burago, D. and Ivanov, S., Isometric embeddings of Finsler manifolds. Algebra i Analiz 5(1993), no. 1, 179–192 (in Russian); translation in St.Petersburg Math. J. 5(1994), no. 1, 159–169.Google Scholar
[5] Cartan, E., Les espaces de Finsler. Actualités Scientifiques et Industrielles, no. 79, Hermann, Paris, 1934.Google Scholar
[6] Chern, S. S. and Shen, Z., Riemann-Finsler Geometry. Nankai Tracts in Mathematics 6, World Scientific, Hackensack, NJ, 2005.Google Scholar
[7] Deicke, A., Über die Finsler-Räume mit Ai = 0, Arch. Math. 4(1953), 45–51. doi:10.1007/BF01899750Google Scholar
[8] Finsler, P., Über Kurven und Flächen in allgemeinen Räumen. Verlag Birkhäuser, Basel, 1951.Google Scholar
[9] Ernic, K., A Guide to Maple. Springer, 1999.Google Scholar
[10] Mo, X. and Yang, C., The explicit construction of Finsler metrics with special curvature properties. Differential. Geom. Appl. 24(2006), no. 2, 119–129. doi:10.1016/j.difgeo.2005.08.004Google Scholar
[11] Nash, J., The immedding problem for Riemannian manifolds. Ann. of Math. 63(1956), 20–63. doi:10.2307/1969989Google Scholar
[12] Shen, Z., Differential Geometry of Spray and Finsler Spaces. Kluwer Academic Publishers, Dordrecht, 2001.Google Scholar
[13] Shen, Z., Finsler metrics with K = 0 and S = 0 . Canad. J. Math. 55(2003), no. 1, 112–132.Google Scholar
[14] Shen, Z., On R-quadratic Finsler spaces. Publ. Math. Debrecen 58(2001), no. 1–2, 263–274.Google Scholar
[15] Shen, Z., On Finsler geometry of submanifolds. Math. Ann. 311(1998), no. 3, 549–576. doi:10.1007/s002080050200Google Scholar