Derivatives with respect to horizontal and vertical lifts of the deformed complete lift metric G_{f} on tangent bundle.

Abstract

In this paper, we define the deformed complete lift metric G_{f} on tangent bundle, which is completely determined by its action on vector fields of type X^{H} and ω^{V}. Later, we obtain the covarient and Lie derivatives applied to the deformed complete lift metric G_{f} with respect to the horizontal and vertical lifts of vector fields, respectively.