Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues |
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Authors: | Giovanni Calvaruso |
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Affiliation: | Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Lecce, Italy |
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Abstract: | We study three-dimensional pseudo-Riemannian manifolds having distinct constant principal Ricci curvatures. These spaces are described via a system of differential equations, and a simple characterization is proved to hold for the locally homogeneous ones. We then generalize the technique used in [O. Kowalski, F. Prüfer, On Riemannian 3-manifolds with distinct constant Ricci eigenvalues, Math. Ann. 300 (1994) 17-28] for Riemannian manifolds and construct explicitly homogeneous and non-homogeneous pseudo-Riemannian metrics in R3, having the prescribed principal Ricci curvatures. |
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Keywords: | 53C50 53C20 53C25 |
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