Real Hypersurfaces in Non-Flat Complex Space form with Structure Jacobi Operator of Lie-Codazzi Type

  • George Kaimakamis
  • Konstantina Panagiotidou
  • Juan de Dios Pérez
Article
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Abstract

In this paper the notion of Lie-Codazzi type of a tensor field T of type (1,1) on real hypersurfaces, which generalizes the notion of Lie parallel, is introduced. Real hypersurfaces in non-flat complex space forms, whose structure Jacobi operator is of Lie-Codazzi type, are studied. More precisely, the non-existence of such real hypersurfaces is proved.

Keywords

Real hypersurface Structure Jacobi operator Lie-Codazzi type Complex projective space Complex hyperbolic space 

Mathematics Subject Classification

Primary 53C40 Secondary 53C15 53D15 

Notes

Acknowledgments

Third author was supported by Grant Proj. No. NRF-2011-220-C0002 from the National Research Foundation of Korea and by MCT-FEDER Grant MTM2010-18099. The authors thank the referees for valuable suggestions in order to improve the paper.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  • George Kaimakamis
    • 1
  • Konstantina Panagiotidou
    • 2
  • Juan de Dios Pérez
    • 3
  1. 1.Faculty of Mathematics and Engineering SciencesHellenic Military AcademyAttikiGreece
  2. 2.Faculty of EngineeringAristotle University of ThessalonikiThessalonikiGreece
  3. 3.Departmento de Geometria y TopologiaUniversidad de GranadaGranadaSpain

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