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On the harmonic rank of a Riemannian structure. (English) Zbl 0797.53011
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 395-402 (1992).
The aim of this paper is to determine the equations which characterize the symmetric spaces of rank \(k\), in the class of all Riemannian symmetric spaces. The harmonic rank of a Riemannian space is defined and the 5-dimensional homogeneous Riemannian manifolds of harmonic rank 2 are classified. The harmonic rank is extended to pseudo-Riemannian spaces and some properties of the Ricci tensor are deduced.
For the entire collection see [Zbl 0764.00002].
Reviewer: A.Neagu (Iaşi)
MSC:
53B20 Local Riemannian geometry
53C35 Differential geometry of symmetric spaces
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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