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On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues

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Complex, Contact and Symmetric Manifolds

Part of the book series: Progress in Mathematics ((PM,volume 234))

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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Authors and Affiliations

  1. Charles University Prague, Czech Republic

    Oldřich Kowalski & Zdeněk Vlášek

Authors
  1. Oldřich Kowalski
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  2. Zdeněk Vlášek
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Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, 186 75, Praha, Czech Republic

    Oldřich Kowalski

  2. Dipartimento di Matematica Pura ed Applicata, Università di L’Aquila, 67100, L’Aquila, Italy

    Emilio Musso

  3. Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, 73100, Lecce, Italy

    Domenico Perrone

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Dedicated to Professor Lieven Vanhecke

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© 2005 Birkhäuser Boston

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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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