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Conformally flat semi-symmetric spaces. (English) Zbl 1114.53027

A semi-symmetric space is a Riemannian manifold \((M,g)\) such that its curvature tensor \(R\) satisfies the condition \(R(X,Y). R =0\). It is well-known that locally symmetric spaces are semi-symmetric but the converse is not true. In the paper the following classification theorem is proved: A conformally flat semi-symmetric space (of dimension \(n>2\)) is either locally symmetric or it is locally irreducible and isometric to a semi-symmetric real cone.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C35 Differential geometry of symmetric spaces
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