On Curvature Inheritance of the Fourth Cartan Tensor in Generalized Fifth-Order Recurrent Finsler Spaces

Abstract

This paper builds upon a new curvature inheritance called curvature inheritance in generalized -fifth recurrent Finsler space. we establish the commutative relationship between the Lie -derivative and the Berwald covariant derivative of the fifth order for . We obtain an equality relation between the Lie-derivative of the Cartan's fourth curvature tensor and  in such space that admits curvature inheritance and curvature inheritance. Furthermore, we prove the force acting on the flow of covariant vector field of fifth order  is opposite to the direction of that vector field's flow and we establish the scalar value of the smooth vector field   under certain conditions.