Annals of Global Analysis and Geometry

, Volume 17, Issue 4, pp 315–328

On Einstein Manifolds of Positive Sectional Curvature

  • Matthew J. Gursky
  • Claude LeBrun

DOI: 10.1023/A:1006597912184

Cite this article as:
Gursky, M.J. & LeBrun, C. Annals of Global Analysis and Geometry (1999) 17: 315. doi:10.1023/A:1006597912184


Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M, g) is ℂℙ2, with its standard Fubini–Study metric.

Einstein manifoldscalar curvaturesectional curvatureWeyl curvature

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Matthew J. Gursky
    • 1
  • Claude LeBrun
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonU.S.A.
  2. 2.Department of MathematicsState University of New YorkStony BrookU.S.A.