Monatshefte für Mathematik

, Volume 177, Issue 4, pp 637–647 | Cite as

Generalized Tanaka–Webster and covariant derivatives on a real hypersurface in a complex projective space

Article

Abstract

We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. For any nonnull constant k and any vector field X tangent to M we can define an operator on M, \(F_X^{(k)}\), related to both connections. We study commutativity problems of these operators and the shape operator of M.

Keywords

g-Tanaka–Webster connection Complex projective space  Real hypersurface kth Cho operators 

Mathematics Subject Classification

53C15 53B25 

Notes

Acknowledgments

This work was supported by grant Proj. No. NRF-2015-R1A2A1A-01002459 from National Research Foundation of Korea. J. de Dios Pérez is partially supported by MEC Project MTM 2010-18099. Y. J. Suh is partially supported by KNU Research Grant, 2013.

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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Departamento de Geometria y TopologiaUniversidad de GranadaGranadaSpain
  2. 2.Department of MathematicsKyungpook National UniversityTaeguRepublic of Korea

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