The real quantum plane as part of 2D-Minkowski space

Using the frame formalism we consider some possible metrics on the real quantum plane. We require that the metric be real and symmetric. In practice this means that we use the freedom of noncommutative geometry to impose a different 'sigma-symmetry', which is chosen so that a complex metric is 'sigma-real' and an un-symmetric metric is 'sigma-symmetric'. The notion of reality and symmetry are changed so that the definition of hermitian does not change. An analysis is then made of a set of possible metrics.