• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.541-545
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• 2007

In this paper, we study the infinitesimal transformation on the fibred Riemannian space. The conharmonic curvature tensor is invariant under the conharmonic transformation. We have proved that the conharmonically flat fibred Riemannian space with totally geodesic fibre is locally the Riemannian product of the base space and a fibre.

• 충청수학회지
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• 제19권4호
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• pp.417-426
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• 2006

In this paper, we are to construct a new fibred Riemannian space with almost complex structure from the lift of an almost contact structures of the base space and that of each fibre. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structure.

• 대한수학회지
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• 제46권1호
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.921-928
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• 1999

K. Kenmotsu introduced and studied the so-called Kenmotsu manifold related to the warped product space. In this paper we charac-terize a Kenmotsu Manifold using the fibred Riemannian space.

• 대한수학회논문집
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• 제12권4호
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• pp.999-1006
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• 1997

We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.441-447
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• 2002

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

• 대한수학회지
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• 제32권3호
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• pp.553-562
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• 1995

In a Recent paper [3], D. Chinea, M. Delon and J. C. Marrero proved that a cosymplectic manifold is formal and constructed an example of compact cosymplectic manifold which is not a global product of a Kaehler manifold with the circle. In this paper we study the compact cosymplectic manifolds with critical Riemannian metrics.