The conjectures on conformal transformations of Riemannian manifolds

Introduction-Let (My g) be a Riemannian manifold. If a Riemannian metric g* on M is related to g as g* =e 2p g for some smooth function p on M, then g* is said to be conformai to g. This relation is obviously an equivalence relation in the set of all the Riemannian metrics on M.