×

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
PDFBibTeX XMLCite