nLab Fubini-Study metric




There is a unique (up to a scalar) hermitian metric on complex projective space, 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.


Last revised on March 1, 2023 at 05:40:42. See the history of this page for a list of all contributions to it.