We construct ρ£ -covariant derivatives in π*π as the generalization of covariant derivative in π*π to £π E. Moreover, we introduce Berwald and Yano derivatives as two important classes of ρ£ -covariant derivatives in π∗π and we study properties of them. Finally, we solve an optimal control problem using some geometric structures and Pontryagin Maximum Principle on Lie algebroids.
