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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
##### Keywords:
harmonic rank; Ricci tensor