# Circle (Riemannian manifold)

## Definition

The **circle**, as a Riemannian manifold, or as an *intrinsic* curve, is defined as a simple closed curve (i.e. diffeomorphic to the circle) satisfying the following equivalent properties:

- Its curvature is constant, and its torsion is zero
- It can be embedded as a submanifold of the plane, as a circle in the plane.