All Questions

Suppose $(M,g, \omega)$ is a Kähler manifold with $\text{Ric}(g) = g$, i.e., $M$ is a Fano manifold. Is $M$ necessarily compact? If not, perhaps complete and Fano implies compact? I'd like to build a ...

A complex manifold $M$ is said to be Fano if the Chern curvature $2$-form is a positive definite $(1,1)$-form. What happens if the Chern curvature $2$-form is a negative definite $(1,1)$-form? What ...

It is well known that the blow-up of $\mathbb P^2$ in one or two points does not accept a Kahler-Einstein metric. Kahler-Einstein metrics are particular cases of constant scalar curvature Kahler ...