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On weakly symmetric and weakly Ricci-symmetric $$K$$-contant manifolds. (English) Zbl 1062.53021
The notions of weakly symmetric and weakly Ricci-symmetric Riemannian manifolds were given and studied by L. Tamássy and T. Q. Binh [Proc. Coll. Differential geometry and its applications, Eger 1989, North. Holland Publ. Comp., Colloq. Math. Soc. János Bolyai 56, 663–670 (1992; Zbl 0791.53021)]. There the compatibility of these conditions with Sasaki type structures was analyzed. In this paper these results are generalized for the case of $$K$$-contact structures. The authors give necessary conditions for the compatibility of several $$K$$-contact structures with weak symmetry, weak Ricci symmetry and almost Einstein properties.

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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