• Corpus ID: 118128548

Generalised Surfaces in ${\Bbb{R}}^3$

@article{Guilfoyle2004GeneralisedSI,
  title={Generalised Surfaces in \$\{\Bbb\{R\}\}^3\$},
  author={Brendan Guilfoyle and Wilhelm Klingenberg},
  journal={arXiv: Differential Geometry},
  year={2004}
}
The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences generated by global sections of $T{\Bbb{P}}^1$ are investigated and a number of theorems are proven that generalise results for closed convex surfaces in ${\Bbb{R}}^3$. 
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