Diagonalization of three-dimensional pseudo-Riemannian metrics

Abstract

We give a short proof of the fact that any Riemannian or Lorentzian real analytic metric in dimension 3 can be locally adapted to the diagonal form. We use the classical Cauchy-Kowalevski Theorem to this purpose:

Keywords

• pseudo-Riemannian metric
• PDE methods
• Cauchy-Kowalevski Theorem