geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
There is a unique (up to a scalar) hermitian metric on complex projective space (which may be normalized), the Fubini-Study metric.
All analytic subvarieties of a complex projective space are in fact algebraic subvarieties and they inherit the Kähler manifold structure from the projective space.
Examples include complex tori $\mathbb{C}^n/L$ where $L$ is a lattice in $\mathbb{C}^n$, K3-surfaces, compact Calabi-Yau manifolds, quadrics, products of projective spaces and so on.
Created on December 21, 2017 at 08:41:33. See the history of this page for a list of all contributions to it.