On Concircular Vector Field and Lie Derivative in Generalized Fifth Recurrent Finsler Space

This paper investigates specific types of concircular motions within a generalized fifth recurrent Finsler space, focusing on Cartan’s fourth curvature tensor Kjkhi in sense of Berwald. We established a new definition for the concircular vector field σh and studied the direction of the force acting on this field using the Lie derivative. In addition, we proved that the concircular vector field σh and the recurrence vector λm are equal under certain condition. The mathematical formulas for the Lie-derivative of recurrence vector λm and Lie-derivative of the product of two concircular vector fields within this space have been obtained. In conclusion, we have provided applications and practical examples that illustrate some of the results.

کلیدواژه ها:

Concircular motion ، Concircular vector field \sigma_h ، Recurrence vector \lambda_m ، Lie-derivative L_v ، Generalized \mathfrak{B}K-fifth recurrent Finsler space