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

Title & Authors
ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS
De, Uday Chand; Mondal, Abul Kalam;

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 $\small{{\beta}}$-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.
Keywords
normal almost contact metric manifolds;non-cosympletic;cyclic parallel Ricci tensor;Einstein manifold;
Language
English
Cited by
1.
D-Homothetic Deformation of Normal Almost Contact Metric Manifolds, Ukrainian Mathematical Journal, 2013, 64, 10, 1514
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