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 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.