Monatshefte für Mathematik

, 158:187 | Cite as

On the structure Jacobi operator of a real hypersurface in complex projective space

  • Hyun Jin Lee
  • Juan de Dios PérezEmail author
  • Florentino G. Santos
  • Young Jin Suh


We prove the non-existence of a certain family of real hypersurfaces in complex projective space. From this result we classify real hypersurfaces whose structure Jacobi operator satisfies a condition that generalizes parallelness.


Complex projective space Real hypersurface Structure Jacobi operator 

Mathematics Subject Classification (2000)

53C15 53B25 


  1. 1.
    Okumura M.: On some real hypersurfaces of a complex projective space. Trans. Am. Math. Soc. 212, 355–364 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Ortega M., Pérez J.D., Santos F.G.: Non-existence of real hypersurfaces with parallel structure Jacobi operator in nonflat complex space forms. Rocky Mountain J. Math. 36, 1603–1613 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Suh Y.J.: A characterization of ruled real hypersurfaces in \({P_n(\mathbb{C})}\) . J. Korean Math. Soc. 29, 351–359 (1992)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Takagi R.: Real hypersurfaces in a complex projective space with constant principal curvatures. J. Math. Soc. Japan 27, 43–53 (1975)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Hyun Jin Lee
    • 1
  • Juan de Dios Pérez
    • 2
    Email author
  • Florentino G. Santos
    • 2
  • Young Jin Suh
    • 1
  1. 1.Department of MathematicsKyungpook National UniversityTaeguRepublic of Korea
  2. 2.Departamento de Geometria y TopologiaUniversidad de GranadaGranadaSpain

Personalised recommendations