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

- Journal title : Communications of the Korean Mathematical Society
- Volume 24, Issue 2, 2009, pp.265-275
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2009.24.2.265

Title & Authors

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

De, Uday Chand; Mondal, Abul Kalam;

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 -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

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