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.
Highlights
Differential transformation D = LX is called as Lie derivation with respect to vector field X ∈ I10(M ) if
The bracket operation of vertical and horizontal vector fields is given by the following formulas:
For all X, Y ∈ I10(M ), f ∈ I00(M ) [5], where R is the Riemannian curvature of g defined by
Summary
Differential transformation D = LX is called as Lie derivation with respect to vector field X ∈ I10(M ) if
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