2013/02/14 by Guojun Yang, Yang, Guojun · 4 citations
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.1302.3300
16 pages
arxiv created 2013/02/14 · openalex publication_date 2013/02/14 · arxiv updated 2013/02/15 · 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 singular Finsler metrics defined by a Riemann metric α and 1-form β and characterize those which are respectively Douglasian and locally projectively flat in dimension n≥ 3 by some equations. Our study shows that the main class induced is an m-Kropina metric plus a linear part on β. For this class with m≠ -1, the local structure of projectively flat case is determined, and it is proved that a Douglas m-Kropina metric must be Berwaldian and a projectively flat m-Kropina metric must be locally Minkowskian. It indicates that the singular case is quite different from the regular one.