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Jeong, Imsoon,Kim, Gyu Jong,Kim, Kyoung Nam Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
Jeong, Imsoon,Perez, Juan De Dios,Suh, Young Jin Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this paper we give a non-existence theorem for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2({\mathbb{C}}^{m+2})$ with re-current normal Jacobi operator ${\bar{R}}_N$.
JEONG, IMSOON,WOO, CHANGHWA The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.3
In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G<sup>*</sup><sub>2</sub>(ℂ<sup>m+2</sup>). Next, we show a non-existence property of real hypersurfaces in G<sup>*</sup><sub>2</sub>(ℂ<sup>m+2</sup>) satisfying such a curvature condition.
ANTI-COMMUTING REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
JEONG, IMSOON,LEE, HYUN JIN,SUH, YOUNG JIN Cambridge University Press 2008 Bulletin of the Australian Mathematical Society Vol.78 No.2
<B>Abstract</B><P>In this paper we give a nonexistence theorem for real hypersurfaces in complex two-plane Grassmannians <I>G</I>2(ℂ<SUP><I>m</I>+2</SUP>) with anti-commuting shape operator.</P>
Jeong, Imsoon,Lee, Hyunjin Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.3
In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.
Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator
Jeong, Imsoon,Suh, Young Jin Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.4
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.
Jeong, Imsoon,Lee, Hyunjin,Suh, Young Jin Springer-Verlag 2015 Annali di matematica pura ed applicata Vol.194 No.3
<P>It is known that submanifolds in Kaehler manifolds have many kinds of connections. Among them, we consider two connections, that is, Levi-Civita and Tanaka-Webster connections for real hypersurfaces in complex two-plane Grassmannians . When they are equal to each other, we give some characterizations in .</P>
Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians
Jeong, Imsoon,Dios Pé,rez, Juan de,Suh, Young Jin,Woo, Changhwa Canadian Mathematical Society 2018 Canadian mathematical bulletin Vol.61 No.3
<B>Abstract</B><P>On a real hypersurface <I>M</I> in a complex two-plane Grassmannian <I>G</I>2() we have the Lie derivation and a differential operator of order one associated with the generalized Tanaka-Webster connection . We give a classification of real hypersurfaces <I>M</I> on <I>G</I>2() satisfying , where ξ is the Reeb vector field on <I>M</I> and <I>S</I> the Ricci tensor of <I>M</I>.</P>
Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator
Jeong, Imsoon,Kim, Seonhui,Jin Suh, Young Canadian Mathematical Society 2014 Canadian mathematical bulletin Vol.57 No.4
<B>Abstract</B><P>In this paper we give a characterization of a real hypersurface of Type (<I>A</I>) in complex two-plane Grassmannians <I>G</I>2(ℂ<SUP>m+2</SUP>), which means a tube over a totally geodesic <I>G</I>2(ℂ<SUP><I>m</I>+1</SUP>) in <I>G</I>2(ℂ<SUP><I>m</I>+2</SUP>), by means of the Reeb parallel structure Jacobi operator ∇<I>ε</I><I>R</I><I>ε</I> = 0.</P>