• Title/Summary/Keyword: non-cosympletic

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ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS

  • De, Uday Chand;Mondal, Abul Kalam
    • Communications of the Korean Mathematical Society
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    • v.24 no.2
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    • pp.265-275
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    • 2009
  • The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.