Kähler–Einstein metric

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 if it admits a Kähler–Einstein metric. The most important special case of these are the Calabi–Yau manifolds, which are Kähler and Ricci-flat.

References

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