2013/02/13 by Guojun Yang, Yang, Guojun · 1 citation
Physics and Astronomy · #53A20 #53B40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1302.3150
openalex publication_date 2013/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, 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 Douglassian, and some families of examples are given for projectively flat classes with β being not closed.