Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues
The Riemannian curvature homogeneous three-spaces have been intensively studied. In his papers [J. Math. Phys. 37, No.~8, 4062--4075 (1996; Zbl 0866.53026) and ibid. 38, No.~2, 1000--1013 (1997; Zbl 0876.53042)], \textit{P. Bueken} studied three-dimensional curvature homogeneous Lorentzian spaces. The author of this paper studies three-dimensional pseudo-Riemannian manifolds having distinct constant principal Ricci curvatures. Also, homogeneous and non-homogeneous pseudo-Riemannian metrics in \(\mathbb R^3\) are explicitly constructed, having prescribed principal Ricci curvatures.
scientific article; zbMATH DE number 5292514