Skip to main content
SpringerLink
Log in

Classification of real hypersurfaces in complex quadric in terms of new tensors

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

In this paper two new tensor fields on real hypersurfaces in complex quadric are introduced. Real hypersurfaces on which the derivatives of the tensor fields with respect to the Levi-Civita connection and the k-th generalized Tanaka–Webster connection of them coincide are studied leading to new classification results on real hypersurfaces in a complex quadric.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Berndt, Y. J. Suh, On the geometry of homogeneous real hypersurfaces in the complex quadric, in Proceedings of the 16th International Workshop on Differential Geometry and the 5th KNUGRG-OCAMI Differential Geometry Workshop, vol. 16 (2012), p. 1–9

  2. J. Berndt, Y.J. Suh, Real hypersurfaces with isometric Reeb flow in complex quadric. Int. J. Math. 24, 1350050 (2013)

    Article  MathSciNet  Google Scholar 

  3. J.T. Cho, CR-structures on real hypersurfaces of a complex space form. Publ. Math. Debr. 54, 473–487 (1999)

    MathSciNet  MATH  Google Scholar 

  4. B. Smyth, Differential geometry of complex hypersurfaces. Ann. Math. 85, 246–266 (1967)

    Article  MathSciNet  Google Scholar 

  5. Y.J. Suh, Real hypersurfaces in the complex quadric with parallel structure Jacobi operator. Differ. Geom. Appl. 51, 33–48 (2017)

    Article  MathSciNet  Google Scholar 

  6. Y.J. Suh, Real hypersurfaces in the complex quadric with commuting and parallel Ricci tensor. J. Geom. Phys. 106, 130–142 (2016)

    Article  MathSciNet  Google Scholar 

  7. Y.J. Suh, Real hypersurfaces in the complex quadric with Reeb parallel shape operator. Int. J. Math. 25, 1450059 (2014)

    Article  MathSciNet  Google Scholar 

  8. Y.J. Suh, D.H. Hwang, Real hypersurfaces in the complex quadric with commuting Ricci tensor. Sci. China Math. 59, 2185–2198 (2016)

    Article  MathSciNet  Google Scholar 

  9. Y.J. Suh, H. Lee, C. Woo, Real hypersurfaces with commuting Jacobi operator in complex quadric. Publ. Math. Debrecen 93, 425–443 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The third author is supported by MINECO-FEDER Project MTM 2016-78807-C2-1-P.

The authors would like to thank the reviewers for their valuable comments which improved the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics and Engineering Sciences, Hellenic Army Academy, 16673, Vari, Attiki, Greece

    George Kaimakamis & Konstantina Panagiotidou

  2. Departamento de Geometria y Topologia and IEMATH, Universidad de Granada, 18071, Granada, Spain

    Juan de Dios Pérez

Authors
  1. George Kaimakamis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Konstantina Panagiotidou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan de Dios Pérez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Kaimakamis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaimakamis, G., Panagiotidou, K. & Pérez, J.d.D. Classification of real hypersurfaces in complex quadric in terms of new tensors. Period Math Hung 83, 250–259 (2021). https://doi.org/10.1007/s10998-021-00383-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-021-00383-0

Keywords

Mathematics Subject Classification

Search

Navigation