# On the structure vector field of a real hypersurface in complex two-plane Grassmannians

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 451-455
- ISSN: 2391-5455

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topCarlos Machado, and Juan Pérez. "On the structure vector field of a real hypersurface in complex two-plane Grassmannians." Open Mathematics 10.2 (2012): 451-455. <http://eudml.org/doc/269420>.

@article{CarlosMachado2012,

abstract = {Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.},

author = {Carlos Machado, Juan Pérez},

journal = {Open Mathematics},

keywords = {Real hypersurfaces; Complex two-plane Grassmannians; Jacobi type vector field; Structure vector field; Killing vector field; real hypersurfaces; complex two-plane Grassmannians; structure vector field},

language = {eng},

number = {2},

pages = {451-455},

title = {On the structure vector field of a real hypersurface in complex two-plane Grassmannians},

url = {http://eudml.org/doc/269420},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Carlos Machado

AU - Juan Pérez

TI - On the structure vector field of a real hypersurface in complex two-plane Grassmannians

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 451

EP - 455

AB - Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.

LA - eng

KW - Real hypersurfaces; Complex two-plane Grassmannians; Jacobi type vector field; Structure vector field; Killing vector field; real hypersurfaces; complex two-plane Grassmannians; structure vector field

UR - http://eudml.org/doc/269420

ER -

## References

top- [1] 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
- [2] 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
- [3] Deshmukh S., Real hypersurfaces of a complex projective space, Proc. Indian Acad. Sci. Math. Sci., 2011, 121(2), 171–179 http://dx.doi.org/10.1007/s12044-011-0027-6 Zbl1269.53060
- [4] Ishihara S., Elementary Riemannian Geometry, Morigita Publ., 1974 (in Japanese)
- [5] Pérez J. de D., Suh Y.J., The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians, J. Korean Math. Soc., 2007, 44(1), 211–235 http://dx.doi.org/10.4134/JKMS.2007.44.1.211 Zbl1156.53034
- [6] Suh Y.J., Real hypersurfaces of type B in complex two-plane Grassmannians, Monatsh. Math., 2006, 147(4), 337–355 http://dx.doi.org/10.1007/s00605-005-0329-9 Zbl1094.53050

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