Three-dimensional Lorentzian manifolds with constant principal Ricci curvatures rho(1)=rho(2)not equal rho(3)

The aim of this paper is the study of (nonhomogeneous) three-dimensional Lorentzian manifolds whose Ricci curvature tensor is diagonalizable with two distinct constant eigenvalues. Two mistakes in a recent paper by D. McManus [J. Math. Phys. 36, 362-369 (1995)] are pointed out and corrected, and a complete (local) classification of the nonhomogeneous manifolds of this type is given, thereby generalizing some results of O. Kowalski [Nagoya Math. J. 132, 1-36 (1993)] to the framework of Lorentzian geometry. (C) 1997 American Institute of Physics.