A CHARACTERIZATION OF THE INFINITESIMAL CONFORMAL TRANSFORMATIONS ON TANGENT BUNDLES

Here, we present a new complete lift metric for whichevery infinitesimal fiber-preserving conformal transformation on thetangent bundle induces an infinitesimal projective transformationon the base manifold. Moreover, this correspondence gives riseto a homomorphism between Lie algebras. Also, we introduce analmost product structure on the tangent bundle and show that itis a product structure if and only if the corresponding Riemannianmetric is of constant curvature.