nLab Fubini-Study metric



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 n/L\mathbb{C}^n/L where LL is a lattice in n\mathbb{C}^n, K3-surfaces, compact Calabi-Yau manifolds, quadrics, products of projective spaces and so on.


Created on December 21, 2017 at 13:41:33. See the history of this page for a list of all contributions to it.