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Start Over Creator Lee, Hyunjin

1. Real hypersurfaces in a complex projective space with pseudo-${\mathbb D}$-parallel structure Jacobi operator

Creator:
Lee, Hyunjin, Pérez, Juan de Dios, and Suh, Young Jin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
real hypersurface and structure Jacobi operator
Language:
English
Description:
We introduce the new notion of pseudo-$\mathbb D $-parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

Creator:
Lee, Hyunjin, Kim, Seonhui, and Suh, Young Jin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
real hypersurface, complex two-plane Grassmannians, Hopf hypersurface, and commuting shape operator
Language:
English
Description:
In this paper, first we introduce a new notion of commuting condition that $\phi \phi _{1} A = A \phi _{1} \phi $ between the shape operator $A$ and the structure tensors $\phi $ and $\phi _{1}$ for real hypersurfaces in $G_2({\mathbb C}^{m+2})$. Suprisingly, real hypersurfaces of type $(A)$, that is, a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in complex two plane Grassmannians $G_2({\mathbb C}^{m+2})$ satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ satisfying the commuting condition. Finally we get a characterization of Type $(A)$ in terms of such commuting condition $\phi \phi _{1} A = A \phi _{1} \phi $.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition. II

Creator:
Lee, Hyunjin, Kim, Seonhui, and Suh, Young Jin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
complex two-plane Grassmannians, Hopf hypersurface, $\mathfrak D^{\bot }$-invariant hypersurface, commuting shape operator, and Reeb vector field
Language:
English
Description:
Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces $M$ of Type ${\rm (A)}$ in complex two plane Grassmannians $G_2({\mathbb C}^{m+2})$ with a commuting condition between the shape operator $A$ and the structure tensors $\phi $ and $\phi _{1}$ for $M$ in $G_2({\mathbb C}^{m+2})$. Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator $A$ and a new operator $\phi \phi _{1}$ induced by two structure tensors $\phi $ and $\phi _{1}$. That is, this commuting shape operator is given by $\phi \phi _{1} A = A \phi \phi _{1}$. Using this condition, we prove that $M$ is locally congruent to a tube of radius $r$ over a totally geodesic $G_2({\mathbb C}^{m+1})$ in $G_2({\mathbb C}^{m+2})$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public