Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

Eunmi Pak; Juan de Dios Pérez; Young Jin Suh

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 569-577
  • ISSN: 0011-4642

Abstract

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We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian G 2 ( ℂ m + 2 ) . In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in G 2 ( ℂ m + 2 ) satisfying such conditions.

How to cite

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Pak, Eunmi, Pérez, Juan de Dios, and Suh, Young Jin. "Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians." Czechoslovak Mathematical Journal 65.2 (2015): 569-577. <http://eudml.org/doc/270099>.

@article{Pak2015,
abstract = {We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_2(\{\mathbb \{C\}\}^\{m+2\})$. In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_2(\{\mathbb \{C\}\}^\{m+2\})$ satisfying such conditions.},
author = {Pak, Eunmi, Pérez, Juan de Dios, Suh, Young Jin},
journal = {Czechoslovak Mathematical Journal},
keywords = {real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; Levi-Civita connection; generalized Tanaka-Webster connection; normal Jacobi operator},
language = {eng},
number = {2},
pages = {569-577},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians},
url = {http://eudml.org/doc/270099},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Pak, Eunmi
AU - Pérez, Juan de Dios
AU - Suh, Young Jin
TI - Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 569
EP - 577
AB - We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_2({\mathbb {C}}^{m+2})$. In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_2({\mathbb {C}}^{m+2})$ satisfying such conditions.
LA - eng
KW - real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; Levi-Civita connection; generalized Tanaka-Webster connection; normal Jacobi operator
UR - http://eudml.org/doc/270099
ER -

References

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