Let (M; g) be a Riemannian manifold and TM be its tangent bundle. In the present paper, we study infinitesimal projective transformations on TM with respect to the Levi-Civita connection of a class of (pseudo-)Riemannian metrics ~g which is a generalization of the three classical lifts of the metric g. We characterized this type of transformations and then we prove that if (TM; ~g) admits a non-affine infinitesimal projective transformation, then M and TM are locally flat.
