nLab Fubini-Study metric

Context

Riemannian geometry

Riemannian geometry

Basic definitions

• Riemannian manifold

• moduli space of Riemannian metrics

• pseudo-Riemannian manifold

• geodesic

• Levi-Civita connection

• Theorems

• Poincaré conjecture-theorem
• Applications

• gravity

• Complex geometry

complex geometry

Contents

Idea

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.

References

Created on December 21, 2017 at 08:41:33. See the history of this page for a list of all contributions to it.