On weakly symmetric Riemannian spaces. (English) Zbl 0922.53018

De, U. C.; Bandyopadhyay, Somnath

Publ. Math. 54, No. 3-4, 377-381 (1999).

Weakly symmetric spaces \((WS)_n\) are those Riemannian spaces in which the covariant derivative of the curvature tensor is a general linear expression of the curvature tensor and several vector fields (this is a generalization of locally symmetric spaces).
In this paper, a simplification of the defining relation of a \((WS)_n\) is given and by a concrete example its existence is exhibited.

Reviewer: Lajos Tamássy (Debrecen)

MSC:

53C35

Differential geometry of symmetric spaces

Keywords:

weakly symmetric Riemannian space; curvature tensor