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On the Riemannian Curvature Tensor of a Real Hypersurface in Complex Two-Plane Grassmannians

  • Juan de Dios PérezEmail author
  • Changhwa Woo
Article
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Abstract

We prove the nonexistence of Hopf real hypersurfaces in complex two-plane Grassmannians such that the covariant derivatives with respect to Levi-Civita and kth generalized Tanaka–Webster connections in the direction of the Reeb vector field applied to the Riemannian curvature tensor coincide when the shape operator and the structure operator commute on the \(\mathcal Q\)-component of the Reeb vector field.

Keywords

Real hypersurfaces Complex two-plane Grassmannians Generalized Tanaka–Webster connection Riemannian curvature tensor Reeb vector field 

Mathematics Subject Classification

Primary 53C40 Secondary 53C15 

Notes

Acknowledgements

First author is partially supported by MCT-FEDER project MTM2013-47828-C2-1-P, and second author is supported by Fostering Core Leaders No. NRF-2013H1A8A1004325.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Department of MathematicsKyungpook National UniversityDaeguRepublic of Korea

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