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On weakly conformally symmetric manifolds. (English) Zbl 1224.53033
A weakly conformally symmetric manifold is a Riemannian manifold whose covariant derivative of its Weyl conformal curvature tensor $$C$$ satisfies certain generalization of recurrence relation. The authors show that an Einstein weakly conformally symmetric manifold reduces to a weakly symmetric manifold. They also consider transformations of a weakly conformally symmetric manifold in a manifold of the same type. Several examples of weakly conformally symmetric manifolds with non-vanishing scalar curvature are constructed.

MSC:
 53B20 Local Riemannian geometry 53B35 Local differential geometry of Hermitian and Kählerian structures 53B05 Linear and affine connections
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