From a given deformed Lorentz transformation in momentum space the corresponding transformations in space‐time are derived by means of canonical methods. A diagonal metric, essentially invariant under these transformations, but dependent on the considered physical objects, is constructed. As a second possibility, the canonical variables are modified in such a way that the metric becomes proportional to the Minkowski metric. This leads to noncanonical Poisson brackets, reminiscent of some versions of deformed Poisson algebras.