Belkhelfa, Mohamed; Deszcz, Ryszard; Verstraelen, Leopold Symmetry properties of 3-dimensional D’Atri spaces. (English) Zbl 1120.53010 Kyungpook Math. J. 46, No. 3, 367-376 (2006). 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. Reviewer: Shen Yi-Bing (Hangzhou) Cited in 2 Documents MSC: 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53B25 Local submanifolds Keywords:Heisenberg space; D’Atri space; Thurston geometry; semi-symmetry; pseudo-symmetry PDFBibTeX XMLCite \textit{M. Belkhelfa} et al., Kyungpook Math. J. 46, No. 3, 367--376 (2006; Zbl 1120.53010)