مسیب زهره وند

Let (Mn, g) be a Riemannian manifold and TMn its tangent bundle. In this paper, firstly, we determine the infinitesimal fiber-preserving projective(IFP) transformations on TMn with respect to the Riemannian connection of the deformed complete lift metric G˜f = gC +(fg)V, where f is a nonzero differentiable function on Mn and gC and gV are the complete lift and the vertical lift of g on TMn, respectively. Then, we prove that (Mn, g) is locally flat, if (TMn, G˜f ) admits a nonaffine infinitesimal fiber-preserving projective transformation. Finally, the infinitesimal complete lift projective transformations on (TMn, G˜f ) are studied.