# Definition:Riemann Surface/Elliptic

## Definition

### Definition 1

A Riemann surface is elliptic if and only if its universal cover is the Riemann sphere.

### Definition 2

A Riemann surface is elliptic if and only if it admits a metric of constant positive curvature.

## Also see

• Results about Riemann surfaces can be found here.

## Source of Name

This entry was named for Georg Friedrich Bernhard Riemann.