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On weak symmetries of Einstein and Sasakian manifolds. (English) Zbl 0849.53038
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 \(\nabla\text{ Ric}\).

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B20 Local Riemannian geometry
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