# Definition:Riemann Surface/Parabolic

## Definition

### Definition 1

A Riemann surface is parabolic if and only if its universal cover is the complex plane.

### Definition 2

A Riemann surface is parabolic if and only if it admits a metric of zero curvature.

## Also see

• Results about Riemann surfaces can be found here.

## Source of Name

This entry was named for Georg Friedrich Bernhard Riemann.