Kähler-Einstein metric

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In differential geometry, a Kähler-Einstein metric on a complex manifold is a Riemannian metric that is both a Kähler metric and an Einstein metric. A manifold is said to be Kähler-Einstein is it admits a Kähler-Einstein metric. The most important special case of these are the Calabi-Yau manifolds, which are Kähler and Ricci-flat.

[edit] References

• Andrei Moroianu, Lectures on Kähler Geometry (2007), London Mathematical Society Student Texts 69, Cambridge ISBN 978-0-521-68897-0.