# nLab Kähler-Einstein manifold

### Context

#### Riemannian geometry

Riemannian geometry

## Basic definitions

• Riemannian manifold

• moduli space of Riemannian metrics

• pseudo-Riemannian manifold

• geodesic

• Levi-Civita connection

• ## Theorems

• Poincaré conjecture-theorem
• ## Applications

• gravity

• #### Complex geometry

complex geometry

## Idea

A Kähler-Einstein manifold is a Riemannian manifold which is both a Kähler manifold as well as an Einstein manifold.

## References

Created on February 9, 2013 at 00:01:26. See the history of this page for a list of all contributions to it.