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Results tagged with kahler-einstein-metric
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user 126348
The Kahler-Einstein metric is an example of a canonical metric on a Kahler manifold. We say that a metric $\omega$ is Kahler-Einstein if $Ric(\omega)=\lambda\omega$, where $\lambda\in\{-1,0,+1\}$.
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The Dirac-Ricci operator
If we consider a spin manifold $M$, we can define the Ricci curvature $Ricc (X,Y)$ which is a symmetric tensor, moreover the spinors are defined, so that we can define a Dirac-Ricci operator:
$$DR(\ps …
- 187
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The hermitian Einstein manifolds
I take an hermitian manifold $(M,g,J)$ and I define from the riemannian curvature $R(X,Y)$ as a $2$-form:
$$
Ricc(J)= \sum_i R(J e_i,e_i)
$$
with $(e_i)$ an orthonormal basis of the tangent.
$$
2R(J)= …
- 187