Spiro, A.; Tricerri, Franco 3-dimensional Riemannian metrics with prescribed Ricci principal curvatures. (English) Zbl 0851.53022 J. Math. Pures Appl., IX. Sér. 74, No. 3, 253-271 (1995). The authors prove that, for any triplet of distinct constants \(\rho_1\), \(\rho_2\), \(\rho_3\), there always exists an analytic Riemannian metric on a domain of \(\mathbb{R}^3\) whose principal Ricci curvatures are constant and equal to the numbers \(\rho_i\). The local equivalence of such metrics is studied and it is proved that the moduli space of their isometry classes depends on an infinite number of parameters. A more recent result by the reviewer and Z. Vlášek says that the moduli space is parametrized by three arbitrary functions of two variables. Reviewer: O.Kowalski (Praha) Cited in 1 ReviewCited in 4 Documents MSC: 53C20 Global Riemannian geometry, including pinching 58D27 Moduli problems for differential geometric structures Keywords:moduli space of isometry classes; principal Ricci curvatures PDFBibTeX XMLCite \textit{A. Spiro} and \textit{F. Tricerri}, J. Math. Pures Appl. (9) 74, No. 3, 253--271 (1995; Zbl 0851.53022)