Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Eunmi Pak; Juan de Dios Pérez; Carlos J. G. Machado; Changhwa Woo

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 207-218
  • ISSN: 0011-4642

Abstract

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We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian G 2 ( ℂ m + 2 ) which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in G 2 ( ℂ m + 2 ) and prove non-existence of real hypersurfaces in G 2 ( ℂ m + 2 ) with generalized Tanaka-Webster parallel normal Jacobi operator.

How to cite

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Pak, Eunmi, et al. "Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator." Czechoslovak Mathematical Journal 65.1 (2015): 207-218. <http://eudml.org/doc/270041>.

@article{Pak2015,
abstract = {We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_2(\{\mathbb \{C\}\}^\{m+2\})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_2(\{\mathbb \{C\}\}^\{m+2\})$ and prove non-existence of real hypersurfaces in $G_2(\{\mathbb \{C\}\}^\{m+2\})$ with generalized Tanaka-Webster parallel normal Jacobi operator.},
author = {Pak, Eunmi, de Dios Pérez, Juan, Machado, Carlos J. G., Woo, Changhwa},
journal = {Czechoslovak Mathematical Journal},
keywords = {real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka-Webster connection; normal Jacobi operator; generalized Tanaka-Webster parallel normal Jacobi operator},
language = {eng},
number = {1},
pages = {207-218},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator},
url = {http://eudml.org/doc/270041},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Pak, Eunmi
AU - de Dios Pérez, Juan
AU - Machado, Carlos J. G.
AU - Woo, Changhwa
TI - Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 207
EP - 218
AB - We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_2({\mathbb {C}}^{m+2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_2({\mathbb {C}}^{m+2})$ and prove non-existence of real hypersurfaces in $G_2({\mathbb {C}}^{m+2})$ with generalized Tanaka-Webster parallel normal Jacobi operator.
LA - eng
KW - real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka-Webster connection; normal Jacobi operator; generalized Tanaka-Webster parallel normal Jacobi operator
UR - http://eudml.org/doc/270041
ER -

References

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