Communications in Mathematical Physics

, Volume 262, Issue 1, pp 177–208 | Cite as

On Eta-Einstein Sasakian Geometry

  • Charles P. BoyerEmail author
  • Krzysztof Galicki
  • Paola Matzeu


A compact quasi-regular Sasakian manifold M is foliated by one-dimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold Open image in new window . In the case when the transverse space Open image in new window is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem in the context of Sasakian geometry to prove the existence of η-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl and Lorenzian Sasakian-Einstein structures.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Charles P. Boyer
    • 1
    Email author
  • Krzysztof Galicki
    • 2
  • Paola Matzeu
    • 3
  1. 1.Department of Mathematics & StatisticsUniversity of New MexicoAlbuquerqueUSA
  2. 2.Max-Planck-Institut für MathematikBonnGermany
  3. 3.Dipartimento di Matematica e InformaticaUniversitá di CagliariCagliariItaly

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