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2015 | 13 | 1 |
Tytuł artykułu

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

Treść / Zawartość
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Języki publikacji
EN
Abstrakty
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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-19
zaakceptowano
2015-04-01
online
2015-05-19
Twórcy
  • Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki
    54124, Greece
  • Departmento de Geometria y Topologia, Universidad de Granada, 18071, Granada, Spain
Bibliografia
  • [1] Berndt J., Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math., 1989, 395,132-141
  • [2] Cho J.T., CR-structures on real hypersurfaces of a complex space form, Publ. Math. Debrecem, 1999, 54, 473-487
  • [3] Cho J.T., Pseudo-Einstein CR-structures on real hypersurfaces of a complex space form, Hokkaido Math. J., 2008, 37, 1-17
  • [4] Ivey T.A., Ryan P.J., The structure Jacobi operator for real hypersurfaces in CP2 and CH2, Results Math., 2009, 56, 473-488
  • [5] Ivey T.A., Ryan P.J., Hopf hypersurfaces of small Hopf principal curvature in CH2, Geom. Dedicata, 2009, 141, 147-161
  • [6] Maeda Y., On real hypersurfaces of a complex projective space, J. Math. Soc. Japan, 1976, 28, 529-540
  • [7] Montiel S., Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan, 1985, 35, 515-535
  • [8] Montiel S., Romero A., On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata, 1986, 20, 245-261
  • [9] Niebergall R., Ryan P.J., Real hypersurfaces in complex space forms, Math. Sci. Res. Inst. Publ., 1997, 32, 233-305
  • [10] Okumura M., On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc., 1975, 212, 355-364
  • [11] Panagiotidou K., Xenos Ph.J, Real hypersurfaces in CP2 and CH2 whose structure Jacobi operator is Lie D-parallel, Note Mat.,2012, 32, 89-99
  • [12] Pérez J.D., Commutativity of Cho and structure Jacobi operators of a real hypersurface in a complex projective space, Ann. diMat. (in press), DOI 10.1007/s10231-014-0444-0[WoS][Crossref]
  • [13] Takagi R., On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math., 1973, 10, 495-506
  • [14] Tanno S., Variational problems on contact Riemannian manifolds, Trans. Am. Math. Soc., 1989, 314, 349-379
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0032
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