 In fact using this version it has been shown that global hyperbolicity is stable under metric perturbations.In 2003, Bernal and Sánchez showed that any globally hyperbolic manifold "M" has a smooth embedded three-dimensional Cauchy surface, and furthermore that any two Cauchy surfaces for "M" are diffeomorphic.In particular, "M" is diffeomorphic to the product of a Cauchy surface with formula_13.