Projective Motions in Generalized Fifth Recurrent Finsler Space via Lie Derivative of Berwald Covariant Tensors

In this paper, we investigate the nature of projective motion within a generalized fifth recurrent Finsler space, denoted as -5 .Utilizing Berwald's connection and higher-order covariant derivatives of Cartan's fourth curvature tensor, we analyze the behavior of projective transformations through the application of the Lie-derivative.A comprehensive system of tensorial identities involving the () -torsion tensor, deviation tensor, and scalar curvature is employed to establish a series of theorems that characterize the projective motion in this setting.Our findings reveal that the Lie-derivatives of higher-order derivatives of the Cartan curvature tensor, as well as associated torsion and curvature tensors, exhibit invariant projective behavior.Additionally, we demonstrate the vanishing of specific curvature-related parameters, including the Berwald connection components and the partial derivatives of the scalar curvature vector.