## 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

### Keywords:

semi-symmetric space
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