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

• Autorzy: Carlos Machado , Juan Pérez
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Real hypersurfaces; Complex two-plane Grassmannians; Jacobi type vector field; Structure vector field; Killing vector field

Kategorie tematyczne

• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
• 53C40: Global submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 451-455

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Carlos Machado

• Universidad de Granada

autor

Juan Pérez

• Universidad de Granada

Bibliografia

• [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
• [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
• [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
• [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
• [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

Identyfikatory

DOI

10.2478/s11533-012-0004-z