All Questions

Is there any direct way of seeing that the space obtained via the Gibbons-Hawking ansatz over $\mathbb{R}^3\setminus\{p_1,p_2\}$ with a suitable choice of complex structure is biholomorphic to $\text{...

A Hermitian manifold $(M,J,g)$ can be defined as a complex manifold $(M,J)$, with integrable complex structure $J$, equipped with a Riemannian metric satisfying $g\circ (J\otimes J) = g$. In this ...

I'm reading several books and articles concerning Yau's proof of the Calabi conjecture. I want to have a deep understading of how and why such proof actually works, but most articles are aimed at ...