• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1375-1397
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• 2014

In this paper we establish codimension reduction theorem for submanifolds of a (4m+3)-dimensional unit sphere $S^{4m+3}$ with Sasakian 3-structure and apply it to submanifolds of a quaternionic projective space.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.109-123
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• 1999

In this paper we prove a reduction theorem of the codimension for real submanifold of quaternionic projective space as a quaternionic analogue corresponding to those in Cecil [4], Erbacher [5] and Okumura [9], and apply the theorem to quaternionic CR- submanifold of quaternionic projective space.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.459-467
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• 1999

A complete analysis of the equation x'=y, y'=$\beta$y-$\alpha$x2+$\alpha$x2+$\delta$xy, where $\alpha$ and $\beta$ small, describing a particular unfolding of the Takens-Bogdanov singularity is presented.

• East Asian mathematical journal
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• v.30 no.1
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• pp.1-14
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• 2014

The first purpose of this paper is to study contact CR submanifolds of Sasakian manifolds and investigate some properties concernig with ${\phi}$-holomorphic bisectional curvature. The second purpose is to show an existence theorem of mixed foliate proper contact CR submanifolds in the standard Sasakian space form $E^{2m+1}$(-3) with constant ${\phi}$-sectional curvature -3.