# Definition:Riemann Surface/Hyperbolic

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## 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.