Skip to main content
SpringerLink
Log in

Isometric immersions from a Kähler manifold into the quaternionic projective space

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this paper we present a rigidity theorem for isometric immersions from Kähler manifolds into a quaternionic projective space (or its non compact real form), when its nullity index is everywhere positive.

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. Alekseevsky, D.V., Marchiafava, S.: Hermitian and Kähler submanifolds of a quaternionic Kähler manifold. Osaka J. Math. 38, 869–904 (2001)

    MathSciNet  MATH  Google Scholar 

  2. Abe, K.: Applications of a Riccati type differential equation to Riemannian manifolds with totally geodesic distributions. Tohoko Math. J. 25, 425–444 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dajczer, M., Rodriguez, L.: On isometric immersions into complex space forms. Math. Ann. 299, 223–230 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eschenburg, J., Ferreira, M.J., Tribuzy, R.: A characterization of the standard embeddings of \(\mathbb{C} P^2\) and \(Q^3\). J. Diff. Geom. 84, 289–300 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Ferus, D.: On the completeness of the nullity foliations. Mich. Math. J. 18, 61–64 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  6. Funabashi, S.: Totally complex submanifolds of a quaternionic Kaehlerian manifold. Kodai Math. J. 2, 314–336 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ishihara, S.: Quaternionic Kahler manifolds. J. Diff. Geom. 9, 483–500 (1974)

    MathSciNet  MATH  Google Scholar 

  8. Marchiafava, S.: Complex submanifolds of quaternionic Kähler manifolds. Contemporary Geometry and Related Topics, pp. 325–335. Univ. Belgrade, Fac. Math., Belgrade (2006)

  9. Tsukada, K.: Parallel submanifolds in a quaternionic projective space. Osaka J. Math. 22, 187–241 (1985)

    MathSciNet  MATH  Google Scholar 

  10. Wolf, J.A.: Elliptic spaces in Grassmann manifolds. Ill. J. Math. 7, 447–462 (1963)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CMAF, Universidade de Lisboa, Lisbon, Portugal

    M. J. Ferreira & B. A. Simões

  2. Universidade Federal do Amazonas, Manaus, Brazil

    R. Tribuzy

Authors
  1. M. J. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. A. Simões
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Tribuzy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. Ferreira.

Additional information

Work supported by FCT (Fundação para a Ciência e Tecnologia) UID/MAT/04561/2013 in Portugal and by CNPq and FAPEAM in Brazil.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferreira, M.J., Simões, B.A. & Tribuzy, R. Isometric immersions from a Kähler manifold into the quaternionic projective space. manuscripta math. 151, 243–254 (2016). https://doi.org/10.1007/s00229-016-0837-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-016-0837-z

Mathematics Subject Classification

Search

Navigation