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3-dimensional Riemannian metrics with prescribed Ricci principal curvatures. (English) Zbl 0851.53022

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)

MSC:

53C20 Global Riemannian geometry, including pinching
58D27 Moduli problems for differential geometric structures
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