Table of Contents
Geometry
Volume 2014 (2014), Article ID 931319, 10 pages
http://dx.doi.org/10.1155/2014/931319
Research Article

A Local Classification of Some Special -Metrics of Constant Flag Curvature

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received 7 May 2014; Accepted 18 July 2014; Published 17 August 2014

Academic Editor: Giovanni Calvaruso

Copyright © 2014 Hongmei Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Bao, C. Robles, and Z. Shen, “Zermelo navigation on Riemannian manifolds,” Journal of Differential Geometry, vol. 66, no. 3, pp. 377–435, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  2. L. Zhou, “A local classification of a class of (α,β) metrics with constant flag curvature,” Differential Geometry and Its Applications, vol. 28, no. 2, pp. 170–193, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Y. Shen and L. Zhao, “Some projectively flat (α,β)-metrics,” Science in China. Series A, vol. 49, no. 6, pp. 838–851, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. Matsumoto, “The Berwald connection of Finsler space with an (α,β)-metric,” Tensor, vol. 50, pp. 18–21, 1991. View at Google Scholar
  5. S. S. Chern and Z. Shen, Riemann-Finsler Geometry, vol. 6 of Nankai Tracts in Mathematics, World Scientific, Hackensack, NJ, USA, 2005.
  6. X. Cheng, Z. Shen, and Y. Tian, “A class of Einstein (α,β)-metrics,” Israel Journal of Mathematics, vol. 192, no. 1, pp. 221–249, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Z. Shen, Diffierential Geometry of Spray and Finsler Spaces, Kluwer Academic, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  8. B. Li, Y. Shen, and Z. Shen, “On a class of Douglas metrics,” Studia Scientiarum Mathematicarum Hungarica: A Quarterly of the Hungarian Academy of Sciences, vol. 46, no. 3, pp. 355–365, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Douglas, “The general geometry of paths,” Annals of Mathematics, vol. 29, no. 1–4, pp. 143–168, 1927/28. View at Publisher · View at Google Scholar · View at MathSciNet