Post Closed as "not a real question" by Deane Yang, Tim Perutz, Misha, Willie Wong, Benoît Kloeckner
3 added 329 characters in body

hallo,

I have the following question: Let $X$ be a Calabi-Yau manifold ($X$ might be compact with or without boundary). How can one prove then that the metric is Ricci flat? I would be very thankfull for answers. My definition of calabi-yau manifolds is: $(X,\omega, \Omega)$ is Calabi-Yau if we have $\frac{\omega^{n}}{n!} = (-1)^{\frac{n(n-1)}{2}} (\frac{i}{2})^{n} \Omega \wedge \bar{\Omega}$, where $\Omega$ is the holomorphic volume form and $\omega$ is the Kähler form. I am wondering if one can show that $\omega$ is then Ricci-flat?

bruno

2 added 48 characters in body

hallo,

I have the following question: Let $X$ be a Calabi-Yau manifold ($X$ might be compact with or without boundary). How can one prove then that the metric is Ricci flat? I would be very thankfull for answers.

bruno

1