Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 3389–3407 | Cite as

Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with Commuting Structure Jacobi Operators

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Abstract

In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field T, that is, \({R_{\xi} \phi T = TR_{\xi} \phi}\), where TA or TS for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. Using simultaneous diagonalization for commuting symmetric operators, we give a complete classification of real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting condition, respectively.

Keywords

Real hypersurfaces complex hyperbolic two-plane Grassmannians Hopf hypersurface shape operator Ricci tensor structure Jacobi operator commuting condition 

Mathematics Subject Classification

Primary 53C40 Secondary 53C15 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Research Institute of Real and Complex ManifoldKyungpook National UniversityDaeguRepublic of Korea
  2. 2.Department of Mathematics and Research Institute of Real and Complex ManifoldKyungpook National UniversityDaeguRepublic of Korea
  3. 3.Department of MathematicsKyungpook National UniversityDaeguRepublic of Korea

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