• Title/Summary/Keyword: $K{\ddot{a}}hler$ structure

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ON THE NORMAL BUNDLE OF A SUBMANIFOLD IN A KÄHLER MANIFOLD

  • Bang, Keumseong
    • Korean Journal of Mathematics
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    • v.5 no.1
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    • pp.75-82
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    • 1997
  • We show that the normal bundle of a Lagrangian submanifold in a K$\ddot{a}$hler manifold has a symplectic structure and provide the equivalent conditions for the normal bundle of such to be K$\ddot{a}$hler.

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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.

DEFORMATION RIGIDITY OF ODD LAGRANGIAN GRASSMANNIANS

  • Park, Kyeong-Dong
    • Journal of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.489-501
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    • 2016
  • In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.

Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator

  • Jeong, Imsoon;Suh, Young Jin
    • Kyungpook Mathematical Journal
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    • v.57 no.4
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    • pp.683-699
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    • 2017
  • We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric $Q^{m*}=SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field N becomes A-principal or A-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^{m*}=SO_{m,2}/SO_mSO_2$ with Killing shape operator.

Real Hypersurfaces with Invariant Normal Jacobi Operator in the Complex Hyperbolic Quadric

  • Jeong, Imsoon;Kim, Gyu Jong
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.551-570
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    • 2020
  • We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Qm∗ = SOom,2/SOmSO2. The invariant normal Jacobi operator implies that the unit normal vector field N becomes 𝕬-principal or 𝕬-isotropic. Then in each case, we give a complete classification of real hypersurfaces in Qm∗ = SOom,2/SOmSO2 with Lie invariant normal Jacobi operators.