Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type

Carlos Machado; Juan Dios Pérez; Imsoon Jeong; Young Suh

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 578-582
  • ISSN: 2391-5455

Abstract

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We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.

How to cite

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Carlos Machado, et al. "Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type." Open Mathematics 9.3 (2011): 578-582. <http://eudml.org/doc/269567>.

@article{CarlosMachado2011,
abstract = {We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.},
author = {Carlos Machado, Juan Dios Pérez, Imsoon Jeong, Young Suh},
journal = {Open Mathematics},
keywords = {Real hypersurfaces; Complex two-plane Grassmannians; Normal Jacobi operator; Codazzi type; real hypersurfaces; complex two-plane Grassmannians; normal Jacobi operator},
language = {eng},
number = {3},
pages = {578-582},
title = {Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type},
url = {http://eudml.org/doc/269567},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Carlos Machado
AU - Juan Dios Pérez
AU - Imsoon Jeong
AU - Young Suh
TI - Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 578
EP - 582
AB - We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.
LA - eng
KW - Real hypersurfaces; Complex two-plane Grassmannians; Normal Jacobi operator; Codazzi type; real hypersurfaces; complex two-plane Grassmannians; normal Jacobi operator
UR - http://eudml.org/doc/269567
ER -

References

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  1. [1] Alekseevskii D.V., Compact quaternion space, Funct. Anal. Appl., 1968, 2(2), 106–114 http://dx.doi.org/10.1007/BF01075944 
  2. [2] Berndt J., Console S., Olmos C., Submanifolds and Holonomy, Chapman Hall/CRC Res. Notes Math., 434, Chapman & Hall/CRC, Boca Raton, 2003 http://dx.doi.org/10.1201/9780203499153 
  3. [3] Berndt J., Suh Y.J., Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 1999, 127(1), 1–14 http://dx.doi.org/10.1007/s006050050018 Zbl0920.53016
  4. [4] Berndt J., Suh Y.J., Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians, Monatsh. Math., 2002, 137(2), 87–98 http://dx.doi.org/10.1007/s00605-001-0494-4 Zbl1015.53034
  5. [5] Jeong I., Kim H.J., Suh Y.J., Real hypersurfaces in complex two-plane Grassmannians with parallel normal Jacobi operator, Publ. Math. Debrecen, 2010, 76(1–2), 203–218 Zbl1274.53080
  6. [6] Kimura M., Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc., 1986, 296(1), 137–149 http://dx.doi.org/10.1090/S0002-9947-1986-0837803-2 Zbl0597.53021
  7. [7] Martínez A., Pérez J.D., Real hypersurfaces in quaternionic projective space, Ann. Mat. Pura Appl., 1986, 145(1), 355–384 http://dx.doi.org/10.1007/BF01790548 Zbl0615.53012

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