• Korean Journal of Mathematics
• /
• 제5권1호
• /
• pp.75-82
• /
• 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.

• 호남수학학술지
• /
• 제35권2호
• /
• pp.147-161
• /
• 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.

• 대한수학회지
• /
• 제53권3호
• /
• pp.489-501
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제57권4호
• /
• pp.683-699
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제60권3호
• /
• pp.551-570
• /
• 2020

We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Q^m∗ = SO^o_m,2/SO_mSO₂. 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 Q^m∗ = SO^o_m,2/SO_mSO₂ with Lie invariant normal Jacobi operators.