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 .