On the spectrum of the curvature operator of a 3-dimensional locally homogeneous Riemannian manifold (Q2799787)
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scientific article; zbMATH DE number 6568568
| Language | Label | Description | Also known as |
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| English | On the spectrum of the curvature operator of a 3-dimensional locally homogeneous Riemannian manifold |
scientific article; zbMATH DE number 6568568 |
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13 April 2016
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curvature operator
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constant eigenvalues
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On the spectrum of the curvature operator of a 3-dimensional locally homogeneous Riemannian manifold (English)
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From results of \textit{O. Kowalski} [Czech. Math. J. 46, No. 3, 427--474 (1996; Zbl 0879.53014); C. R. Acad. Sci., Paris, Sér. I 311, No. 6, 355--360 (1990; Zbl 0713.53028)] follows that for any triple \((\sigma_{23},\sigma_{31},\sigma_{12})\in\mathbb{R}^3\) there exists a 3-dimensional Riemannian manifold such that the curvature operator acting on bivectors, has the preassigned constant eigenvalues \((\sigma_{23},\sigma_{31},\sigma_{12})\). However, one can not find for any such triple a 3-dimensional locally homogeneous Riemannian manifold with this property. In this paper a criterion is obtained for the existence of such a locally homogeneous Riemannian manifold.NEWLINENEWLINEFor the entire collection see [Zbl 1298.53003].
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