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## Osculating planes of a curve

Differential Geometry
Grigorios Kostakos
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### Osculating planes of a curve

Let $\overrightarrow{r}:I\subseteq\mathbb{R}\longrightarrow\mathbb{R}^3$ be a regular parametrized curve with the property that all its osculating planes pass through a fixed point. Show that $\overrightarrow{r}$ is a plane curve.
Grigorios Kostakos