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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 β-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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참고문헌 (8)
참고문헌 신청
A. Gray / 1978 / Einstein-like manifolds which are not Einstein / Geom. Dedicata 7 (3) : 259 ~ 280
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry, Lecture Note in Mathematics / Springer-Verlag
D. E. Blair / 1976 / The theory of quasi Sasakian structures / J. Differ. Geometry 1 : 331 ~ 345
D. E. Blair / 2002 / Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics / Birkhauser Boston , Inc.
D. Janssen / 1981 / Almost contact structures and curvature tensors / Kodai Math. J. 4 : 1 ~ 27
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry, Lecture Note in Mathematics / Springer-Verlag
D. E. Blair / 1976 / The theory of quasi Sasakian structures / J. Differ. Geometry 1 : 331 ~ 345
D. E. Blair / 2002 / Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics / Birkhauser Boston , Inc.
D. Janssen / 1981 / Almost contact structures and curvature tensors / Kodai Math. J. 4 : 1 ~ 27
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