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Ali Taghavi
Ali Taghavi
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Is there a simple smooth closed curve $\gamma$ in $\mathbb{R}^{3}$ such that for all $x,y\in \gamma$ with $x \neq y $, $l_{x}$ and $l_{y}$ are skew lines skew lines, where $l_{x} $ and $l_{y}$ are straight lines tangent to $\gamma$ at $x,y$, respectively? What about real analytic case?

Is there a simple smooth closed curve $\gamma$ in $\mathbb{R}^{3}$ such that for all $x,y\in \gamma$ with $x \neq y $, $l_{x}$ and $l_{y}$ are skew lines, where $l_{x} $ and $l_{y}$ are straight lines tangent to $\gamma$ at $x,y$, respectively? What about real analytic case?

Is there a simple smooth closed curve $\gamma$ in $\mathbb{R}^{3}$ such that for all $x,y\in \gamma$ with $x \neq y $, $l_{x}$ and $l_{y}$ are skew lines, where $l_{x} $ and $l_{y}$ are straight lines tangent to $\gamma$ at $x,y$, respectively? What about real analytic case?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

A very torsioned closed curve in space

Is there a simple smooth closed curve $\gamma$ in $\mathbb{R}^{3}$ such that for all $x,y\in \gamma$ with $x \neq y $, $l_{x}$ and $l_{y}$ are skew lines, where $l_{x} $ and $l_{y}$ are straight lines tangent to $\gamma$ at $x,y$, respectively? What about real analytic case?