**Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 16, pp. 65-71 (2000)
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On weakly symmetric and weakly Ricci-symmetric $K$-contact manifolds

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U. C. De, T. Q. Binh and A. A. Shaikh

T. Q. Binh: Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, P.O. Box 12, Hungary, binh@math.klte.hu; U. C. De and A. A. Shaikh, Department of Mathematics, University of Kalyani, Kalyani-741235, W.B., India, ucde@klyuniv.ernet.in.

**Abstract:** In this paper we shall give necessary conditions for the compatibility of several $K$-contact structures with weak symmetry and weak Ricci-symmetry and weak Ricci-symmetry, provided they do not reduce to the common local symmetry, that is, they are proper. Thus weak symmetry and weak Ricci-symmetry are weaker than pseudosymmetry and pseudo Ricci-symmetry respectively.

**Keywords:** Weakly symmetric Riemannian manifold, K-contact manifold

**Classification (MSC91):** 53C15; 53C25

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