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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.

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