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Can we foliate the space $\mathbb{R}^3$ with Frenet curves whose tangent and normal vectores span a given $2$ dimensional distribution?
Let $D$ be a $2$ dimensional distribution of $\mathbb{R}^3$.
Is there a $1$ dimensional foliation of $\mathbb{R}^3$ with Frenet curves such that for every leaf $\gamma$ of the foliation we have $\...
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