Caratheodory curve

Definition

A Caratheodory curve is a closed $C^{3}$-smooth curve in $\mathbb {R} ^{3}$ with nonvanishing curvature.

Relation with other properties

Stronger properties

• Barner curve

Facts

Sedykh's theorem

Further information: Sedykh's theorem

Any Caratheodory curve has at least four flattenings.