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Symmetry properties of 3-dimensional D’Atri spaces. (English) Zbl 1120.53010
In this paper, the authors study the semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds such as the D’Atri spaces, the Thurston geometries as well as the $$\eta$$-Einstein manifolds by means of the classical tensor analysis. It is proved that all these manifolds are pseudo-symmetric and many of them are not semi-symmetric.

##### MSC:
 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53B25 Local submanifolds