• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.953-961
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• 2002

Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.3
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• pp.89-94
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• 2002

The present paper mainly treats with almost f-cosymplectic manifolds. This notion contains almost cosymplectic and almost Kenmotsu manifolds. Almost cosymplectic manifolds introduced in ［1］ have been studied by many schalors, say ［2］, ［3］, ［4］, and almost Kenmotsu manifolds introduced in ［5］ have been studied in ［6］, ［7］. The present paper studies some geometrical and topological properties of the canonical foliation defined by the contact distribution of an almost f-cosymplectic manifold. The purpose of the present paper is to extend the results obtained in ［8］, ［9］.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.129-134
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• 2004

It is well known that the warped product $L\;{\times}\;{_f}\;F$ of a line L and a Kaehler manifold F is an almost contact Riemannian manifold which is characterized by some tensor equations appeared in (1.7) and (1.8). In this paper we determine contact slant submanifolds tangent to the structure vector field of $L\;{\times}\;{_f}\;F$.