Skip to main content
SpringerLink
Log in

Traceless component of the conformal curvature tensor in Kähler manifold

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension ⩾ 4, and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on p (0 ⩽ p ⩽ 2)-forms on the manifold by using the traceless component.

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. M. Berger, P. Gauduchon et E. Mazet: Le Spectre d’une Variété Riemannienne. Lecture Notes in Mathematics 194, Springer-Verlag, 1971.

  2. H. Kitahara, K. Matsuo and J. S. Pak: A conformal curvature tensor field on hermitian manifolds; Appendium. J. Korean Math. Soc.; Bull. Korean Math. Soc. 27 (1990), 7–17; 27–30.

    MATH  MathSciNet  Google Scholar 

  3. D. Krupka: The trace decomposition problem. Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry 36 (1995), 303–315.

    MATH  MathSciNet  Google Scholar 

  4. J. S. Pak, K.-H. Cho and J.-H. Kwon: Conformal curvature tensor field and spectrum of the Laplacian in Kaehlerian manifolds. Bull. Korean Math. Soc. 32 (1995), 309–319.

    MATH  MathSciNet  Google Scholar 

  5. V. K. Patodi: Curvature and the fundamental solution of the heat operator. J. Indian Math. Soc. 34 (1970), 269–285.

    MathSciNet  Google Scholar 

  6. S. Tachibana: Riemannian Geometry. Asakura Shoten, Tokyo, 1967. (In Japanese.)

    Google Scholar 

  7. S. Tanno: Eigenvalues of the Laplacian of Riemannian manifolds. Tôhoku Math. J. 25 (1973), 391–403.

    MATH  MathSciNet  Google Scholar 

  8. Gr. Tsagas: On the spectrum of the Laplace operator for the exterior 2-forms. Tensor N. S. 33 (1979), 94–96.

    MATH  MathSciNet  Google Scholar 

  9. S. Yamaguchi and G. Chuman: Eigenvalues of the Laplacian of Sasakian manifolds. TRU Math. 15 (1979), 31–41.

    MATH  MathSciNet  Google Scholar 

  10. K. Yano: Differential Geometry on complex and almost complex spaces. Pergamon Press, New York, 1965.

    MATH  Google Scholar 

  11. K. Yano and S. Ishihara: Kaehlerian manifolds with constant scalar curvature whose Bochner curvature tensor vanishes. Hokkaido Math. J. 3 (1974), 297–304.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Nippon Institute of Technology, Minami-Saitama Gun, Saitama, 345-8501, Japan

    S. Funabashi

  2. Department of Computational Mathematics, School of Computer Aided Science, Inje University, Kimhae, 621-749, Korea

    H. S. Kim & Y.-M. Kim

  3. Department of Mathematics Education, Silla University, Busan, 617-736, Korea

    Y.-M. Kim

  4. Department of Mathematics Education, Kyungpook National University, Daegu, 702-701, Korea

    J. S. Pak

Authors
  1. S. Funabashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. S. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y.-M. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. S. Pak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Shigeru Ishihara on the occasion of his 82nd birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Funabashi, S., Kim, H.S., Kim, YM. et al. Traceless component of the conformal curvature tensor in Kähler manifold. Czech Math J 56, 857–874 (2006). https://doi.org/10.1007/s10587-006-0061-1

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-006-0061-1

Keywords

Search

Navigation