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

Brendan Guilfoyle; Wilhelm Klingenberg

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

Brendan Guilfoyle·Wilhelm Klingenberg

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Abstract

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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Brendan Guilfoyle, Wilhelm Klingenberg. 2004-06-09. Generalised Surfaces in ${\Bbb{R}}^3$. https://arxiv.org/abs/math/0406185

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