On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let (M,g) be an n-dimensional Riemannian manifold, and TM be its tangent bundle with the liftmetricG . Then every infinitesimal fiber-preserving conformal transformation X induces an infinitesimalhomothetic transformation V on M . Furthermore, the correspondence X ¨V gives a homomorphism ofthe Lie algebra of infinitesimal fiber-preserving conformal transformations on TM onto the Lie algebra ofinfinitesimal homothetic transformations on M , and the kernel of this homomorphism is naturallyisomorphic onto the Lie algebra of infinitesimal isometries of M .