2013/02/17 by Guojun Yang, Yang, Guojun
Mathematics · Physics and Astronomy · #53A20 #53B40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A20 #msc:53B40
paper · pdf · doi:10.48550/arxiv.1302.4120
21 pages. arXiv admin note: substantial text overlap with arXiv:1302.3150, arXiv:1302.3300
arxiv created 2013/02/17 · openalex publication_date 2013/02/17 · arxiv updated 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Singular Finsler metrics, such as Kropina metrics and m-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of two-dimensional singular Finsler metrics defined by a Riemann metric α and 1-form β, and we characterize those which are Douglasian or locally projectively flat by some equations. It shows that the main class induced is an m-Kropina metric plus a linear part on β. For this class, the local structure of Douglasian or (in part) projectively flat case is determined, and in particular we show that a Kropina metric is always Douglasian and a Douglas m-Kropina metric with m≠ -1 is locally Minkowskian. It indicates that the two-dimensional case is quite different from the higher dimensional ones.