3-dimensional Riemannian metrics with prescribed Ricci principal curvatures (Q1914532)

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.