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In this study, firstly, the k-th order extension of complex product manifoldis consid- ered. Then the higher order vertical, complete lifts of geometricstructures on product manifold to its extended spaces are given. Also higherorder lifts of tensor field of type (1,1) are presented. And then extendedcontact manifolds are defined. Finally higher order vertical and complete liftsof time dependent complex Hamiltonian equations on contact manifold to itsextensions are introduced. In conclusion, geometric meaning of Hamiltonianmechanical systems is discussed.

Lifts of Time Dependent Complex Hamiltonian Mechanical Systems