Abstract

In this paper, we begin by introducing the exponential change of $m$-th root Finsler metrics, referred to as exponentially transformed $m$-th root Finsler metric. For this metric, we derive the fundamental metric tensors along with their inverses. Additionally, we determine the spray coefficients and establish the conditions under which the transformed metric is projectively related to an $m$-th root metric. Furthermore, we investigate the conditions for the transformed Finsler space to exhibit locally duality flatness and projective flatness. We also identify the conditions under which the transformed metrics to be the Berwald metric, weakly Berwald metric, Landsberg metric, and weakly Landsberg metric. Lastly, we show that every exponential change of $m$-th root Finsler metrics with almost vanishing $H$-curvature has vanishing $H$-curvature.

Keywords: Finsler space; Exponential transformation; $m$-th root metric; projectively related metrics; locally dually flat metric; $H$-curvature.

MSC: 53B40, 53C60

DOI: 10.57016/MV-ZCVH1064

Pages:  1--14