On conformal diffeomorphisms between product Riemannian manifolds (Q5902998)

Let M and \(M^*\) be connected manifolds of dimension \(n\geq 3\), with Riemannian metrics g and \(g^*\) and product structures F and G respectively. One says that F and G commute at a point P of M with respect to a diffeomorphism f of M to \(M^*\), if \(F\circ f^*G=f^*G\circ F\) at P. The author proves the following theorem: If both M and \(M^*\) are complete Riemannian product manifolds, then there is no global conformal diffeomorphism of M onto \(M^*\) such that the product structures F and G do commute with respect to it in an open subset of M.