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Czechoslovak Mathematical Journal

, Volume 65, Issue 2, pp 569–577 | Cite as

Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

  • Eunmi Pak
  • Juan de Dios Pérez
  • Young Jin Suh
Article

Abstract

We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian G 2(ℂ m+2). In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in G 2(ℂ m+2) satisfying such conditions.

Keywords

real hypersurface complex two-plane Grassmannian Hopf hypersurface Levi-Civita connection generalized Tanaka-Webster connection normal Jacobi operator 

MSC 2010

53C40 53C15 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  • Eunmi Pak
    • 1
  • Juan de Dios Pérez
    • 2
  • Young Jin Suh
    • 1
  1. 1.Department of MathematicsKyungpook National UniversityDaeguRepublic of Korea
  2. 2.Departmento de Geometría y Topología, Facultad de CienciasUniversidad de GranadaGranadaSpain

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