Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Konstantina Panagiotidou; Juan de Dios Pérez

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page Article ID 1550075, 14 p.-Article ID 1550075, 14 p.
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Konstantina Panagiotidou, and Juan de Dios Pérez. "Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms." Open Mathematics 13.1 (2015): Article ID 1550075, 14 p.-Article ID 1550075, 14 p.. <http://eudml.org/doc/270916>.

@article{KonstantinaPanagiotidou2015,
abstract = {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.},
author = {Konstantina Panagiotidou, Juan de Dios Pérez},
journal = {Open Mathematics},
keywords = {Real hypersurfaces; Structure Jacobi operator; Cho operator; Non-flat complex space forms; real hypersurfaces; Jacobi operators; parallelism; complex hyperbolic two-plane Grassmannians},
language = {eng},
number = {1},
pages = {Article ID 1550075, 14 p.-Article ID 1550075, 14 p.},
title = {Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms},
url = {http://eudml.org/doc/270916},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Konstantina Panagiotidou
AU - Juan de Dios Pérez
TI - Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - Article ID 1550075, 14 p.
EP - Article ID 1550075, 14 p.
AB - 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.
LA - eng
KW - Real hypersurfaces; Structure Jacobi operator; Cho operator; Non-flat complex space forms; real hypersurfaces; Jacobi operators; parallelism; complex hyperbolic two-plane Grassmannians
UR - http://eudml.org/doc/270916
ER -

References

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  12. [12] Pérez J.D., Commutativity of Cho and structure Jacobi operators of a real hypersurface in a complex projective space, Ann. di Mat. (in press), DOI 10.1007/s10231-014-0444-0 [WoS][Crossref] Zbl1329.53047
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  14. [14] Tanno S., Variational problems on contact Riemannian manifolds, Trans. Am. Math. Soc., 1989, 314, 349-379 Zbl0677.53043

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