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

  • Published : 2009.04.30

Abstract

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.

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Cited by

  1. D-Homothetic Deformation of Normal Almost Contact Metric Manifolds vol.64, pp.10, 2013, https://doi.org/10.1007/s11253-013-0732-7
  2. Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator vol.6, pp.11, 2018, https://doi.org/10.3390/math6110246