• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.373-391
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• 2007

We study an (n+3)($n\;{\geq}\;7-dimensional$ real submanifold of a (4m+3)-unit sphere $S^{4m+3}$ with Sasakian 3-structure induced from the canonical quaternionic $K\"{a}hler$ structure of quaternionic (m+1)-number space $Q^{m+1}$, and especially determine contact three CR-submanifolds with (p-1) contact three CR-dimension under the equality conditions given in (4.1), where p = 4m - n denotes the codimension of the submanifold. Also we provide necessary conditions concerning sectional curvature in order that a compact contact three CR-submanifold of (p-1) contact three CR-dimension in $S^{4m+3}$ is the model space $S^{4n_1+3}(r_1){\times}S^{4n_2+3}(r_2)$ for some portion $(n_1,\;n_2)$ of (n-3)/4 and some $r_1,\;r_2$ with $r^{2}_{1}+r^{2}_{2}=1$.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.79-86
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• 1998

In this paper, we study an (n ＋ 1)-dimensional compact, orientable, minimal contact CR-submanifold of (n - 1) ontact CR-dimension in a (2m ＋ 1)-dimensional unit sphere $S^{2m＋1}$ in terms of integral formula.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.561-577
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• 1998

We study (n＋3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of $S^{4r＋3}$(a) $\times$ $S^{4s＋3}$(b) ($a^2$＋ $b^2$=1, 4(r ＋ s) = n - 3) as a contact three CR sub manifold of a (4m＋3)-dimensional unit sphere.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.109-116
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• 2007

We study an (n+1)($(n{\geq}3)$-dimensional contact CR-submanifold of (n-1) contact CR-dimension in a (2m+1)-unit sphere $S^{2m+1}$, and to determine such sub manifolds under conditions concerning the second fundamental form and the induced almost contact structure.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.777-787
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• 2005

In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.215-222
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• 2015

We show that homology group on a contact CR-warped product submanifold in odd dimensional sphere is zero under certain conditions in terms of warping function and the dimension of the submanifold.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.131-140
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• 2014

In this paper we investigate (n+1)($n{\geq}3$)-dimensional contact CR-submanifolds M of (n-1) contact CR-dimension in a complete simply connected Sasakian space form of constant ${\phi}$-holomorphic sectional curvature $c{\neq}-3$ which satisfy the condition h(FX, Y)+h(X, FY) = 0 for any vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of M, respectively.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.585-600
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• 2011

In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.