2013/10/13 by Guojun Yang, Yang, Guojun · 1 citation
Physics and Astronomy · #53B40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1310.3460
openalex publication_date 2013/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In particular, we show that all p-power metrics but Randers metrics, square metrics and 2-dimensional square-root metrics, are always Ricci-flat-parallel. Further, the local structure is almost determined for 2-dimensional square-root metrics which are Einsteinian (equivalently, of isotropic flag curvature), and examples show such metrics are not necessarily Ricci-flat.