Planar curve

Definition

A planar curve is a one-dimensional connected Riemannian manifold (in other words, a curve) satisfying the following equivalent conditions:

• The torsion is zero at all points
• The curve can be embedded as a Riemannian submanifold of the plane: in other words, it can be viewed as a curve in the plane, inheriting the Riemannian metric from the plane