On quasi-conformally flat weakly Ricci symmetric manifolds. (English) Zbl 1164.53011

The authors obtain certain properties of (pseudo-)Riemannian manifolds which are weakly Ricci symmetric and simultaneously quasi-conformally flat. The reader must be careful because the formulations of the theorems are not complete. For instance, Theorem 1 states that the Ricci tensor is of rank 1. In this theorem, it is in fact additionally assumed that \(\delta\neq0\), which eliminates a large subclass of the considered manifolds. Moreover, the examples are not well described. For instance, the metric in Example 1 is Ricci recurrent, which contradicts Theorem 11, where the non-Ricci recurrence of this metric is asserted.


53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B35 Local differential geometry of Hermitian and Kählerian structures
53B05 Linear and affine connections
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