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Communications in Mathematical Physics

, Volume 125, Issue 4, pp 637–642 | Cite as

Complete Ricci-flat Kähler manifolds of infinite topological type

  • Michael T. Anderson
  • Peter B. Kronheimer
  • Claude LeBrun
Article

Abstract

We display an infinite dimensional family of complete Ricci-flat Kähler manifolds of complex dimension 2, for which the second homology is infinitely generated. These are obtained from the Gibbons-Hawking Ansatz [2] by using infinitely many, sparsely distributed centers.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Ergeb. Math.,3. Folge, Bd 4. Berlin, Heidelberg, New York: Springer 1984Google Scholar
  2. 2.
    Gibbons, G., Hawking, S.: Gravitational multi-instantons. Phys. Lett.78B, 430–432 (1978)Google Scholar
  3. 3.
    Hitchin, N.: Polygons and gravitons. Math. Proc. Camb. Phil. Soc.85, 465–476 (1979)Google Scholar
  4. 4.
    Hitchin, N., Karlhede, A., Lindstrom, U., Rocek, M.: Hyperkähler metrics and supersymmetry. Commun. Math. Phys.108, 535–589 (1987)Google Scholar
  5. 5.
    Kronheimer, P.: Instantons gravitationelles et singularites de Klein. C. R. Acad. Sci. Paris303, Ser. I 53–55 (1986)Google Scholar
  6. 6.
    Kronheimer, P.: A Torelli type theorem for gravitational instantons. J. Diff. Geo.29, 3 (1989)Google Scholar
  7. 7.
    Sha, J.-P., Yang, D.G.: Metrics of positive Ricci curvature on connected sums ofS n×S m (preprint)Google Scholar
  8. 8.
    Yau, S.-T.: Problem section, seminar on differential geometry. Ann. Math. Studies, Vol. 102. Princeton: Princeton University Press 1982Google Scholar
  9. 9.
    Yau, S.-T.: Nonlinear analysis in geometry. L'Enseignement Math.33, 109–156 (1987)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Michael T. Anderson
    • 1
  • Peter B. Kronheimer
    • 2
    • 3
  • Claude LeBrun
    • 1
  1. 1.Department of MathematicsSUNY at Stony BrookStony BrookUSA
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  3. 3.Merton CollegeOxfordUnited Kingdom

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