Definition:Riemann Surface/Hyperbolic

Definition

Definition 1

A Riemann surface is hyperbolic if and only if its universal cover is the unit disk.

Definition 2

A Riemann surface is hyperbolic if and only if it admits a metric of constant negative curvature.

Also see

• Results about Riemann surfaces can be found here.

Source of Name

This entry was named for Georg Friedrich Bernhard Riemann.