Osculating planes of a curve
Posted: Wed Aug 31, 2016 4:47 pm
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.