• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.265-275
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• 2001

In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

• East Asian mathematical journal
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• v.24 no.4
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• pp.421-429
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• 2008

We study invariant lightlike submanifolds and almost contact CR-lightlike submanifolds of an indefinite cosymplectic manifold.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1173-1192
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• 2013

We introduce CR, SCR and GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature $c$ and of constant type ${\alpha}$. We also prove characterization theorems on the existence of totally umbilical and minimal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.25-32
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• 2012

We define a quarter symmetric metric connection in a Lorentzia para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.575-586
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• 2001

The purpose of this paper is to study n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$, and especially to determine such submanifolds under some curvature conditions.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.

• East Asian mathematical journal
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• v.25 no.4
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• pp.495-504
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• 2009

We introduce three classes of quaternion lightlike submanifolds, screen real lightlike submanifolds and CR lightlike submanifolds of an indefinite quaternion Kaehlerian manifold and study the geometry of leaves of their distributions.

• 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.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.107-118
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• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.965-977
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• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.