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

Abstract

Let (, ) M g be an n-dimensional Riemannian manifold, and TM be its tangent bundle with the lift metric G . Then every infinitesimal fiber-preserving conformal transformation X induces an infinitesimal homothetic transformation V on M . Furthermore, the correspondence XV → gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on TM onto the Lie algebra of infinitesimal homothetic transformations on M , and the kernel of this homomorphism is naturally isomorphic onto the Lie algebra of infinitesimal isometries of M .