(alpha, beta)-metrics form a rich class of computable Finsler metrics. They play an important role in Finsler geometry. In this work, we study a class of Finsler metric in the form F = alpha exp(s), where beta is a Riemannian metric and is a 1-form. We call F exponential Finsler metric. We show that every exponential (alpha, beta)-metrics is a weakly Landsberg metric if and only if it is a Berwald metric.
