Article contents
A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2014
References
[BC]
Bácsό, S., Cheng, X., and Shen, Z., Curvature properties of -metrics. In: Finsler geometry, Sapporo 2005, Advanced Studies in Pure Mathematics, 48, Math. Soc. Japan, Tokyo, 2007, pp. 73–110.Google Scholar
[BCS]
Bao, D., Chern, S. S., and Shen, Z., An introduction to Riemann-Finsler geometry. Graduate Texts in Mathematics, 200, Springer-Verlag, New York, 2000.Google Scholar
[C]
Chavel, I., Riemannian geometry. A modern introduction. Second ed., Cambridge Studies in Advanced Mathematics, 98, Cambridge University Press, Cambridge, 2006.Google Scholar
[Ch]
Cheeger, J., Finiteness theorems for Riemannian manifolds. Amer. J. Math.
92 (1970), 61–74. http://dx.doi.org/10.2307/2373498
Google Scholar
[CS]
Chern, S.-S. and Shen, Z., Riemann-Finsler geometry. Nankai Tracts in Mathematics, 6, World Scientific Publishing Co., Hackensack, NJ, 2005.Google Scholar
[E]
Egloff, D., Uniform Finsler Hadamard manifolds. Ann. Inst. H. Poincaré Phys. Thér. 66 (1997), no. 3, 323–357.Google Scholar
[HK]
Heintze, E. and Karcher, H., A general comparison theorem with applications to volume estimates forsubmanifolds.Ann. Sci. Ecole Norm. Sup. (4) 11 (1978), no. 4,451–470.Google Scholar
[K]
Klingerberg, W., Contributions to Riemannian geometry in the large. Ann. of Math. (2) 69 (1959), 654–666. http://dx.doi.org/10.2307/1970029
Google Scholar
[Ru]
Rund, H., The theory of subspaces of a Finsler space. I. Math. Z. 56 (1952), 363–375. http://dx.doi.org/10.1007/BF01686755
Google Scholar
[S]
Shen, Z., Lectures on Finsler geometry. World Scientific Publishing, Singapore, 2001.Google Scholar
[W]
Y.Wu, B., Volume form and its applications in Finsler geometry. Publ. Math. Debrecen 78 (2011), no. 3–4, 723–741. http://dx.doi.org/10.5486/PMD.2011.4998
Google Scholar