• Title, Summary, Keyword: QR-submanifold

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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.

CERTAIN CLASS OF QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IN QUATERNIONIC SPACE FORM

  • Kim, Hyang Sook;Pak, Jin Suk
    • Honam Mathematical Journal
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    • v.35 no.2
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    • pp.147-161
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    • 2013
  • In this paper we determine certain class of $n$-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form, that is, a quaternionic K$\ddot{a}$hler manifold of constant Q-sectional curvature under the conditions (3.1) concerning with the second fundamental form and the induced almost contact 3-structure.

SLANT SUBMANIFOLDS OF QUATERNION KAEHLER MANIFOLDS

  • Sahin, Bayram
    • Communications of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.123-135
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    • 2007
  • This paper has two objectives. The first objective is to study slant submanifolds of quaternion Kaehler manifolds. We give characterization theorems and examples of slant submanifolds. For the second objective, we introduce the notion of semi-slant submanifolds which are different from the definition of N. Papaghiuc [15]. We obtain characterization theorems, examples of semi-slant sub manifolds and investigate the geometry of leaves of distributions which are involved in the definition of semi-slant submanifolds.