paraholomorphically projective vector fields on the tangent bundle with the deformed complete lift metric

Let (m_n,g) be a riemannian manifold and tm_n its tangent bundle. in this paper, we determine the fiber-preserving paraholomorphically projective vector fields on tm_n with respect to the levi-civita connection the deformed complete lift metric tilde{g}_f=g^c+(fg)^v, where f is a nonzero differentiable function on m_n and g^c and g^v are the complete lift and the vertical lift of g on tm_n, respectively.