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ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS
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 Title & Authors
ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS
De, Uday Chand; Mondal, Abul Kalam;
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 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
1.
D-Homothetic Deformation of Normal Almost Contact Metric Manifolds, Ukrainian Mathematical Journal, 2013, 64, 10, 1514  crossref(new windwow)
 References
1.
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Note in Mathematics, Vol. 509, Springer-Verlag, Berlin-New York, 1976

2.
D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Vol. 203, Birkhauser Boston , Inc., Boston, 2002

3.
D. E. Blair, The theory of quasi Sasakian structures, J. Differ. Geometry 1 (1976), 331–345

4.
F. Cantrijnt, M. De Leon, and E. A. Lacomha, Gradient vector fields in cosympletic manifolds, J. Phys. A. Math. Gen. 25 (1992), 409–416

5.
A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), no. 3, 259–280 crossref(new window)

6.
D. Janssen and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), 1–27 crossref(new window)

7.
U. H. Ki and H. Nakagawa, A characterization of the Cartan hypersurface in a sphere, Tohoku Math. J. 39 (1987), 27–40 crossref(new window)

8.
Z. Olszak, Normal almost contact manifolds of dimension three, Annales Pol. Math. XLVII (1986), 41–50