Tamássy, L.; Binh, T. Q. On weak symmetries of Einstein and Sasakian manifolds. (English) Zbl 0849.53038 Tensor, New Ser. 53, 140-148 (1993). In a previous paper, the authors called a Riemannian manifold \(M\) weakly symmetric if \(\nabla R\) can be expressed by the curvature tensor \(R\) in a certain way involving a number of 1-forms [Colloq. Math. Soc. János Bolyai 56, 663-670 (1992; Zbl 0791.53021)]. If, in addition, \(M\) is either Einstein or Sasakian, then a linear relation between these 1-forms is deduced. Analogous results hold under the same weak symmetry assumption on \(\nabla\text{ Ric}\). Reviewer: W.Kühnel (Stuttgart) Cited in 5 ReviewsCited in 41 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53B20 Local Riemannian geometry Keywords:Einstein manifold; Sasakian manifold; Ricci tensor; weakly symmetric Riemannian manifold; curvature tensor Citations:Zbl 0791.53021 PDF BibTeX XML Cite \textit{L. Tamássy} and \textit{T. Q. Binh}, Tensor, New Ser. 53, 140--148 (1993; Zbl 0849.53038) OpenURL