Sasaki – Einstein Manifolds and Volume Minimisation

  title={Sasaki – Einstein Manifolds and Volume Minimisation},
  author={Dario Martelli and James F. Sparks and S T Yau},
We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi–Yau cone X, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat– Heckman formula… CONTINUE READING
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