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

100%
Machado C., Dios Pérez J., Jeong I., Suh Y.
Open Mathematics
|
2011
|
tom 9
|
nr 3
578-582
EN
We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.
2
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Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

100%
Panagiotidou K., Pérez J. d. D.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.
3
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Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

100%
de Dios Pérez J., Suh Y. J., Woo C.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.
4
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On the structure vector field of a real hypersurface in complex two-plane Grassmannians

88%
Machado C., Pérez J.
Open Mathematics
|
2012
|
tom 10
|
nr 2
451-455
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.
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