On Locally Projectively Flat Finsler Space of a Special Exponential Metric with Constant Flag Curvature - Tripathi, Brijesh Kumar; Khan, Sadika (Armenian Journal of Mathematics, 2024)
From the point of view of Hilbert's fourth problem, Finsler metrics on an open subset of $\mathbb{R}^n$ with positive geodesics that are straight lines are known as locally projectively flat Finsler metrics. In this article, we have studied such projectively flat $(α,β)$-metrics in the form of the special exponential Finsler metric, where $α$ is a Riemannian metric and $β$ is a differential 1-form. We found that the special exponential metric is locally projectively flat if and only if $α$ is locally projectively flat and $β$ is parallel with respect to $α$. Furthermore, we obtained the flag curvature and proved that the special exponential metric is locally Minkowskian.