Existence and classification of three-dimensional Lorentzian manifold with prescribed distinct Ricci eigenvalues

Abstract

We prove that there exists at least one three-dimensional Lorentzian manifold with any prescribed distinct Ricci eigenvalues, which are given as arbitrary real analytic functions. Moreover, we prove that such Lorentzian manifolds depend locally on three arbitrary functions of two variables.

Keywords

• Lorentzian manifold
• Principal Ricci curvatures
• Partial differential equation
• Cauchy-Kowalevski theorem