The 0-Homogenous Complete Lift Metric

The complete lift of a Riemannian metric g on a differentiable manifold M is not 0-homogeneous on the fibers of the tangent bundle TM. In this paper we introduce a new kind of lift G of g, which is 0-homogeneous. It determines a pseudo-Riemannian metric on ${widetilde {TM}}$ , which depends only on the metric g. We obtain the Levi-Civita connection of this metric and study conformal vector fields on ( ${widetilde {TM},G}$ ). Finally, we introduce the almost product and complex structures which preserve homogeneity and study certain geometrical properties of these structures.