Skip to main content
SpringerLink
Log in

On Nearly-Kähler Geometry

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We consider complete nearly-Kähler manifolds with a canonicalHermitian connection. We prove some metric properties of strict nearly-Kähler manifolds and give a sufficient condition for the reducibility of the canonical Hermitian connection. A holonomic condition for a nearly-Kähler manifold to be a twistor space over a quaternionic-Kähler manifold is given. This enables us to give classification results in 10-dimensions.

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. Alexandrov, B., Grantcharov, G. and Ivanov, S.: Curvature properties of twistor spaces of quaternionic Kähler manifolds, J. Geom. 62 (1998), 1-12.

    Google Scholar 

  2. Belgun, F. and Moroianu, A.: Nearly Kähler 6-manifolds with reduced holonomy, Ann. Global Anal. Geom. 19 (2001), 307-319.

    Google Scholar 

  3. Besse, A.: Einstein Manifolds, Springer, New York, 1987.

    Google Scholar 

  4. Eels, J. and Salamon, S.: Constructions twistorielles des applications harmoniques, C. R. Acad. Sci. Paris 296 (1983), 685-687.

    Google Scholar 

  5. Friedrich, Th. and Ivanov, S.: Parallel spinors and connections with skew-symmetric torsion in string theory, Math. DG/0102142, 2001.

  6. Gray, A.: Nearly Kähler manifolds, J. Differential Geom. 4 (1970), 283-309.

    Google Scholar 

  7. Gray, A.: Weak holonomy groups, Math. Z. 125 (1971), 290-300.

    Google Scholar 

  8. Gray, A.: Riemannian manifolds with geodesic symmetries of order 3, J. Differential Geom. 7 (1972), 343-369.

    Google Scholar 

  9. Gray, A.: The structure of nearly Kähler manifolds, Math. Ann. 223 (1976), 233-248.

    Google Scholar 

  10. Gray, A. and Hervella, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), 35-58.

    Google Scholar 

  11. Grunewald, R.: Six-Dimensional Riemannian manifolds with real Killing spinors, Ann. Global Anal. Geom. 8 (1990), 43-59.

    Google Scholar 

  12. Kirichenko, V. F.: K-spaces of maximal rank, Mat. Zametki 22(4) (1977), 465-476.

    Google Scholar 

  13. LeBrun, C. and Salamon, S.: Strong rigidity of positive quaternion-Kähler manifolds, Invent. Math. 118 (1994), 109-132.

    Google Scholar 

  14. LeBrun, C.: Fano manifolds, contact structures and quaternionic geometry, Internat. J. Math. 6 (1995), 419-437.

    Google Scholar 

  15. Muskarov, O.: Structures presque Hermitiennes sur les espaces twistoriels et leurs types, C. R. Sci. Paris Ser. I Math. 305 (1987), 365-398.

    Google Scholar 

  16. Poon, Y. S. and Salamon S.: Eight-dimensional quaternion Kähler manifolds with positive scalar curvature, J. Differential Geom. 33 (1990), 363-378.

    Google Scholar 

  17. Salamon, S.: Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 143-171.

    Google Scholar 

  18. Swann, A.: Weakening holonomy, Preprint ESI No. 816, 2000.

Download references

Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université de Neuchâtel, rue E. Argand 11, 2007, Neuchâtel, Switzerland

    Paul-Andi Nagy

Authors
  1. Paul-Andi Nagy
    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

Nagy, PA. On Nearly-Kähler Geometry. Annals of Global Analysis and Geometry 22, 167–178 (2002). https://doi.org/10.1023/A:1019506730571

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019506730571

Search

Navigation