• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.157-165
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• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.243-257
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• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.

• 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.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.695-708
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• 2003

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

• 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.

• 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.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.224-236
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• 2024

This study inspects the structure of CR-product of a holomorphic statistical manifold. Findings concerning geodesic submanifolds and totally geodesic foliations in the context of dual connections have been demonstrated. The integrability of distributions in CR-statistical submanifolds has been characterized. The statistical version of CR-product in the holomorphic statistical manifold has been researched. Additionally, some assertions for curvature tensor field of the holomorphic statistical manifold have been substantiated.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.883-899
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• 2014

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.503-519
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• 2000

It is well-known that an analytic generic CR submainfold M of codimension m in Cn+m is locally transformed by a biholomorphic mapping to a plane Cn$\times$Rm ⊂ Cn$\times$Cm whenever the Levi form L on M vanishes identically. We obtain such a normalizing biholomorphic mapping of M in terms of the defining function of M. Then it is verified without Frobenius theorem that M is locally foliated into complex manifolds of dimension n.