# Definition:Riemann Surface/Elliptic

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## 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.