# How can i find such surface?

Let $M\subset\mathbb{R}^{3}$ be a surface of class $C^{r}, r\geq 4$. Define the parabolic set by $P=\{q\in M: K(q)=0\}$, where $K$ is the Gaussian Curvature of $M$.

Let $\gamma:\mathbb{S}^{1}\rightarrow\mathbb{R}^{3}$ be a biregular curve (non zero curvature). Show that there exists a surface $M$, immersed when $\gamma$ is not embedded, such that $\gamma(\mathbb{S}^{1})\subset M$ and $\gamma(\mathbb{S}^{1})$ is a connected component of the parabolic set of $M$.

I dont even know how to start.

Thanks

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