2017/05/31 by Xiaoyun Tang, Tang, Xiaoyun, Changtao Yu +1 · 1 citation
Physics and Astronomy · #53B40 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1705.11111
openalex publication_date 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case ‖β‖α>1 is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Randers metrics (‖β‖α<1). Based on some famous Einstein-Lorentz metrics in General Relativity, such as Minkowski metric, Sitter metric, anti de Sitter metric, Schwarzschild metric, Kerr metric, C-metric, Kasner metric, Levi-Civita metric, Cartor-Novotný-Horský metric, etc., many non-regular Einstein-Randers metrics are constructed. Besides, we find that the case ‖β‖α≡1 is very distinctive. These metrics will be called singular Randers metrics or parabolic Finsler metrics since their indicatrixs are parabolic hypersurface. A preliminary discussion for such metrics is provided.