Skip to main content
SpringerLink
Log in

On the spectral geometry for the Jacobi operators of harmonic maps into a quaternionic projective space

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We characterize both invariant and totally real immersions into the quaternionic projective space by the spectra of the Jacobi operator. Also, we study spectral characterization of harmonic submersions when the target manifold is the quaternionic projective space.

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. Chen, B. Y.: Totally umbilical submanifolds of quaternion space form, J. Austral. Math. Soc. (Series A) 26 (1978), 154–164.

    Google Scholar 

  2. Donnelly, H.: Spectral invariants of the second variation operator, Illinois J. Math. 21 (1977), 185–189.

    Google Scholar 

  3. Fuglede, B.: Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978) 107–144.

    Google Scholar 

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

    Google Scholar 

  5. Gilkey, P. B.: Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Publish or Perish, 1984.

  6. Hasegawa, T.: Spectral geometry of closed minimal submanifolds in a space form, real and complex, Kodai Math. J. 3 (1980), 224–252.

    Google Scholar 

  7. Ishihara, S.: Quaternion Kähler manifolds, J. Differential Geom. 9 (1974), 483–500.

    Google Scholar 

  8. Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), 215–229.

    Google Scholar 

  9. Nishikawa, S., Tondeur, P. and Vanhecke, L.: Spectral geometry for Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 291–304.

    Google Scholar 

  10. Pak, J. S. and Kang, T. H.: Planar geodesic submanifolds in a quaternionic projective space, Geom. Dedicata 26 (1988), 139–155.

    Google Scholar 

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

    Google Scholar 

  12. Urakawa, H.: Spectral geometry of the second variation operator of harmonic maps, Illinois J. Math. 33 (2) (1989), 250–267.

    Google Scholar 

  13. Urakawa, H.: Calculus of Variations and Harmonic Maps (in Japanese), Shokabo, Tokyo, 1990.

    Google Scholar 

  14. Wolf, J. A.: Elliptic space in Grassmann manifolds, Illinois J. Math. 7 (1963), 447–462.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ulsan, 680-749, Ulsan, Korea

    Tae Ho Kang

  2. Department of Mathematics, Kyungpook National University, 702-701, Taegu, Korea

    Jin Suk Pak

Authors
  1. Tae Ho Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin Suk Pak
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, T.H., Pak, J.S. On the spectral geometry for the Jacobi operators of harmonic maps into a quaternionic projective space. Geom Dedicata 60, 153–161 (1996). https://doi.org/10.1007/BF00160620

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00160620

Mathematics Subject Classification (1991)

Key words

Search

Navigation