On weak symmetries of Einstein and Sasakian manifolds. (English) Zbl 0849.53038

Tamássy, L.; Binh, T. Q.

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)

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