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On weakly concircular symmetric manifolds. (English) Zbl 1199.53057
Summary: The object of the present paper is to introduce a type of non-flat Riemannian manifold called ”weakly concircular symmetric manifold” and study its geometric properties as well as its decomposibility. Among others it is shown that every weakly concircular symmetric manifold of vanishing scalar curvature is a weakly symmetric manifold. Also it is proved that in a decomposable weakly concircular symmetric manifold the decompositions are concircularly recurrent. The existence of such a manifold is ensured by several interesting examples.

53B35 Local differential geometry of Hermitian and Kählerian structures
53B05 Linear and affine connections