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Semisymmetric curvature operators and Riemannian \(4\)-spaces elementarily classified. (English) Zbl 0871.53036

Z. Szabó was the first who made a general classification of semi-symmetric Riemannian spaces (i.e., Riemannian manifolds satisfying the curvature identity \(R(X,Y)\cdot R = 0\)). The introductory, algebraic part of this classification is using Kostant’s theorem and other nontrivial results. In this paper an elementary method is given how to reproduce (roughly) the Szabó classification in dimension \(n = 4\).
Reviewer: O.Kowalski (Praha)

MSC:

53C20 Global Riemannian geometry, including pinching
15A75 Exterior algebra, Grassmann algebras
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C35 Differential geometry of symmetric spaces
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