• Title, Summary, Keyword: quaternionic projective space

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CODIMENSION REDUCTION FOR REAL SUBMANIFOLDS OF QUATERNIONIC PROJECTIVE SPACE

  • Kwon, Jung-Hwan;Pak, Jin-Suk
    • 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.

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QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IN QUATERNIONIC PROJECTIVE SPACE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • Journal of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.655-672
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    • 2005
  • The purpose of this paper is to study n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and to give sufficient conditions in order for such a submanifold to be a tube over a quaternionic invariant submanifold.

SOME CURVATURE CONDITIONS OF n-DIMENSIONAL QR-SUBMANIFOLDS OF (p-1) QR-DIMENSION IN A QUATERNIONIC PROJECTIVE SPACE QP(n+p)/4

  • Pak, Jin-Suk;Sohn, Won-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.613-631
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    • 2003
  • The purpose of this paper is to study n-dimensional QR-submanifolds of (p - 1) QR-dimension in a quaternionic projective space $QP^{(n+p)/4}$ and especially to determine such submanifolds under the curvature conditions appeared in (5.1) and (5.2).

REAL n-DIMENSIONAL QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IMMERSED IN QP(n+p)/4

  • Kim, Hyang-Sook;Kwon, Jung-Hwan;Pak, Jin-Suk
    • Communications of the Korean Mathematical Society
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    • v.24 no.1
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    • pp.111-125
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    • 2009
  • The purpose of this paper is to study n-dimensional QR-submanifolds of (p-1) QR-dimension immersed in a quaternionic projective space $QP^{(n+p)/4}$ of constant Q-sectional curvature 4 and especially to determine such submanifolds under the additional condition concerning with shape operator.

ISOPARAMETRIC FUNCTIONS IN S4n+3

  • Jee, Seo-In;Lee, Jae-Hyouk
    • The Pure and Applied Mathematics
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    • v.21 no.4
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    • pp.257-270
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    • 2014
  • In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.