Skip to main content
SpringerLink
Log in

Group actions, gauge transformations, and the calculus of variations

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

References

  1. Atiyah, M., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond., A308, 523–615 (1982)

    Google Scholar 

  2. Berger, M., Ebin, D.: Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Differ. Geom.3, 370–392 (1969)

    Google Scholar 

  3. Besse, A.L.: Einstein manifolds. Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  4. Coron, J.M., Hélein, F.: Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry. Compos. Math.69, 175–228 (1989)

    Google Scholar 

  5. Doi, H., Matsumoto, Y., Matumoto, T.: An explicit formula of the metric on the moduli space of BPST-instantons overS 4. A Fete of Topology. Boston, MA: Academic Press 1988

    Google Scholar 

  6. Earle, C.J., Eells, J.: A fibre bundle description of Teichmüller theory. J. Differ. Geom.3, 19–43 (1969)

    Google Scholar 

  7. Ebin, D.: The manifold of Riemannian metrics. In: Global Analysis. (Proc. Symp. Pure Math., vol. 15, pp. 11–40) Providence, RI: Am. Math. Soc. 1970

    Google Scholar 

  8. Fischer, A.E., Tromba, A.J.: On a purely “Riemannian” proof of the structure and dimension of the unramified moduli space of a compact Riemann surface. Math. Ann.267, 311–345 (1984)

    Google Scholar 

  9. Fischer, A.E., Tromba, A.J.: On the Weil-Petersson metric on Teichmüller spaces. Trans. Am. Math. Soc.284, 319–335 (1984)

    Google Scholar 

  10. Flaschel, D., Klingenberg, W.: Riemannsche Hilbertmannigfaltigkeiten. Periodische Geodätische. (Lect. Notes Math., vol. 282) Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  11. Freed, D.S., Groisser, D.: The basic geometry of the manifold of Riemannian metrics and its quotient by the diffeomorphism group. Mich. Math. J.36, 323–344 (1989)

    Google Scholar 

  12. Gil-Medrano, O., Michor, P.W.: The Riemannian manifold of all Riemannian metrics. (Preprint)

  13. Goldman, W.: The symplectic nature of fundamental groups of surfaces. Adv. Math.54, 200–225 (1984)

    Google Scholar 

  14. Groisser, D., Parker, T.H.: The Riemannian geometry of the Yang-Mills moduli space. Commun. Math. Phys.112, 669–689 (1987)

    Google Scholar 

  15. Habermann, L.: On the geometry of the space ofSp(1) instantons with Pontrjagin index 1 on the 4-sphere. Ann. Global Anal. Differ. Geom.6, 3–29 (1988)

    Google Scholar 

  16. Hitchin, N.: The self-duality equations on a Riemann surface. Proc. Lond. Math. Soc.55, 59–126 (1987)

    Google Scholar 

  17. Itoh, M.: Geometry of anti-self-dual connections and Kuranishi map. J. Math. Soc. Japan40, 9–32 (1988)

    Google Scholar 

  18. Jost, J.: Harmonic maps and curvature computations in Teichmüller theory. Ann. Acad. Sci. Fenn., Series A.I. Math.16, 13–46 (1991)

    Google Scholar 

  19. Jost, J.: Nonlinear methods in Riemannian and Kählerian geometry. (DMV Seminar, Bd. 10) Basel Boston: Birkhäuser 1988

    Google Scholar 

  20. Jost, J., Peng, X.W.: The geometry of moduli spaces of stable vector bundles over Riemann surfaces. Global differential geometry and global analysis. (Lect. Notes Math. Vol. 1481). Springer 1991

  21. Jost, J., Schoen, R.: On the existence of harmonic diffeomorphisms between surfaces. Invent. Math.66, 353–359 (1982)

    Google Scholar 

  22. Schoen, R., Uhlenbeck, K.: A regularity theory for harmonic maps. J. Differ. Geom.17, 307–335 (1982); Correction. ibid. Schoen, R., Uhlenbeck, K.: A regularity theory for harmonic maps. J. Differ. Geom.18, 329 (1983)

    Google Scholar 

  23. Siu, S.T.: Curvature of the Weil-Petersson metric in the moduli space of compact Kähler-Einstein manifolds of negative first Chern class. (Aspects Math., vol. 9, pp. 261–298) Braunschweig Wiesbaden: Vieweg and Sohn 1986

    Google Scholar 

  24. Tromba, A.J.: On an natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric. Manuscr. Math.56, 475–497 (1986)

    Google Scholar 

  25. Tromba, A.J.: On an energy function for the Weil-Petersson metric on Teichmüller space. Manuscr. Math.59, 249–260 (1987)

    Google Scholar 

  26. Valli, G.: Harmonic gauges on Riemann surfaces and stable bundles. Ann. Inst. Henri Poincaré6, 233–245 (1989)

    Google Scholar 

  27. Wolf, M.: The Teichmüller theory of harmonic maps. J. Differ. Geom.29, 449–479 (1989)

    Google Scholar 

  28. Wolpert, S.: Chern forms and the Riemann tensor for the moduli space of curves. Invent. Math.85, 119–145 (1986)

    Google Scholar 

  29. Zograf, P.G., Takhtadzhyan, L.A.: On the geometry of moduli spaces of vector bundles over a Riemann surface. Math. USSR, Izv.35, 83–101 (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, W-4630, Bochum 1, Germany

    Jürgen Jost & Xiao-Wei Peng

Authors
  1. Jürgen Jost
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Wei Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author was supported by various research projects of the DFG

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jost, J., Peng, XW. Group actions, gauge transformations, and the calculus of variations. Math. Ann. 293, 595–621 (1992). https://doi.org/10.1007/BF01444737

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444737

Keywords

Search

Navigation