Summary
In this paper, we deal with 3-dimensional Riemannian manifolds where some conditions are put on their principal Ricci curvatures. In Section 2 we classify locally all Riemannian 3-manifolds with prescribed distinct Ricci eigenvalues, which can be given as arbitrary real analytic functions. In Section 3 we recall, for the constant distinct Ricci eigenvalues, an explicit solution of the problem, but in a more compact form than it was presented in [17]. Finally, in Section 4 we give a survey of related results, mostly published earlier in various journals. Last but not least, we compare various PDE methods used for solving problems of this kind.
The authors have been partly supported by the grant GAČR 201/02/0616 and by the project MSM 113200007.
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Dedicated to Professor Lieven Vanhecke
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Kowalski, O., Vlášek, Z. (2005). On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues. In: Kowalski, O., Musso, E., Perrone, D. (eds) Complex, Contact and Symmetric Manifolds. Progress in Mathematics, vol 234. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4424-5_13
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