Abstract:In this paper, we investigate Almost Rational Finsler (AR-Finsler) metrics, a class of Finsler metrics whose fundamental tensor admits a decomposition $g_{ij}(x,y)=\eta(x,y)a_{ij}(x,y),$ where $\eta$ is a positive smooth function and $a_{ij}$ is rational in the fiber variables. We derive necessary and sufficient conditions for local dual flatness and local projective flatness of AR-Finsler metrics. Furthermore, we obtain a compatibility relation characterizing AR-Finsler metrics that are simultaneously locally dually flat and locally projectively flat. As an application, we establish a rigidity result for AR-Finsler. Motivated by these results and several known rigidity phenomena in special classes of Finsler metrics, we formulate a conjecture concerning the local Minkowskianity of AR-Finsler metrics that are both locally dually flat and locally projectively flat. Several examples are presented to illustrate the theory.
From: Ranadip Gangopadhyay [view email]
[v1]
Sun, 14 Jun 2026 09:27:57 UTC (11 KB)
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