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The Scientific World Journal
Volume 2013 (2013), Article ID 291491, 11 pages
http://dx.doi.org/10.1155/2013/291491
Research Article

On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics

Department of Mathematics, Sichuan University, Chengdu 610064, China

Received 1 August 2013; Accepted 22 August 2013

Academic Editors: P. Mira and O. Mokhov

Copyright © 2013 Guojun Yang. 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.

Abstract

We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α, β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes with β being not closed.